Transcript Shape4-Constructx
Slide 1
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 2
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 3
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 4
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 5
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 6
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 7
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 8
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 9
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 10
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 11
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 12
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 13
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 14
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 15
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 2
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 3
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 4
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 5
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 6
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 7
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 8
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 9
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 10
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 11
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 12
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 13
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 14
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.
Slide 15
MATHEMATICS
Constructions
Aims of the Lesson
• To learn how to construct triangles.
• To learn how to bisect lines at right angles.
• To learn how to bisect angles.
Triangles
• The types of constructions are denoted using S to stand
for side and A to stand for angle.
• SAS means you are given two side lengths and the angle
between them.
• ASA means you are given the base’s length and the angle
at each end of it.
• SSS means you are given all three sides (but no angles)
SAS Triangles
• Draw the longest side (using a ruler).
• At one end of the base, measure the angle given (using a
protractor).
• Draw a line at this angle, equal to the length of the other
side quoted (using a ruler).
• Now join the other end of the base line to the other end of
this second side (using a ruler).
SAS Triangles
• STEP 4:
2:
1:
3:
• Now
At one
Draw
join
the
a
end
line
the
longest
of
atother
the
thisside
base,
angle,
end of
the base
measure
(using
equal
to
a ruler).
the
line
thelength
angle
to the of
given
other
the
(using
other
end
ofside
a
this
protractor).
quoted
second(using
side
a ruler).a ruler).
(using
ASA Triangles
• Draw the side given as the base (using a ruler).
• At one end measure one of the angles.
• Draw a LONG FEINT line at this angle.
• At the other end, measure the other angle.
• Draw a line at this angle that meets the feint line you just
drew.
• Now darken the other side’s line from the base to the third
side (but do NOT rub out the rest of the feint line – these
are your workings/construction lines!)
ASA Triangles
• STEP 6:
1:
3:
4:
5:
2:
Now
the
otheras
• At
Draw
thedarken
one
the
a
other
end
LONG
line
side
measure
at
end,
given
this
FEINT
side’s
line
from
the
the base
line
measure
angle
one
at
ofthat
this
the(using
the
meets
angles.
angle.
other
athe
base
to the
ruler).line
angle.
feint
youthird
justside
(but do NOT rub out
drew.
the rest of the feint
line – these are your
workings/construction
lines!)
SSS Triangles
STEP 4:
3:
1:
• Finally,
Drawset
Now
the
draw
the
longest
compasses
linesside
from to
(using
the
each
length
end
a ruler).
of
ofthe
thebase
third to
side,
put the
the
cross-over
point atpoint
the other
of the
STEP
2:
end of
arcs,
but
thedobase
NOTand
rubdraw
out
a
feint
arc
arc
lines
to cross
– these
the
first
• your
Set
the
compasses
to are
the
arc.
your
lengthworkings/
of the second side,
construction
put the point lines!
at one end of
the base and draw a feint
long arc.
What is a perpendicular bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Perpendicular means at right angles;
• Therefore a perpendicular bisector is a line
that cuts the original line into 2 equal
halves, and also crosses it at 90°
Perpendicular Bisectors
• You will be given a line.
• Set your compass so that they
are equal to about ¾ of the
length of the line.
• Put the point of the compass at
one end of the line and draw a
feint arc above and below the
line.
Perpendicular Bisectors
• Put the point of the compass at
the other end of the line and
draw feint arcs which cross over
the previous two arcs.
• Now draw a straight line through
both cross-over points (but do
NOT rub out your arcs).
• This line is at right angles to the
original line and cuts the original
line in half – perpendicular
bisector!
What is an angle bisector?
• A bisector cuts something into 2 (bi) equal
sections (sector);
• Therefore an angle bisector is a line that
cuts the original angle into 2 equal halves.
Angle Bisector
• You will be given an angle
between two lines.
• Set your compasses at a
length of about 3-4cm
• Put the point of the
compass at the point of the
angle and draw an arc
through each line forming
the angle.
Angle Bisector
• Put the point of the compass at
each of these cross-over points
and draw an arc from each
which cross-over each other.
• Now draw a line from the
original angle’s point through the
last cross-over point (but do
NOT rub out any of your arcs).
• This line has cut the original
angle in half and is therefore the
angle bisector!
What next?
• Print out the notes called Shape4. Read through them and
make sure you answer any questions.
• Work through the MyMaths lesson and then its online
homework called:
• Shape > Constructions > Constructing Triangles found at:
• http://app.mymaths.co.uk/276-resource/constructing-triangles
• http://app.mymaths.co.uk/276-homework/constructing-triangles
• You have now completed this module of work. Revise and then
ask your teacher to email you the assessment to complete and
return via email to your VLE teacher.