Transcript Constructing_triangles_SSS - Chartwell

Teach GCSE Maths
Constructing Triangles SSS
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Teach GCSE Maths
Constructing
Triangles
SSS
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To do the exercises in this presentation you will need
a ruler, compasses and protractor.
We are going to draw some triangles as accurately as
possible.
You need to be able to draw and measure lines
accurate to 1 mm. and angles accurate to 1 degree.
Could you draw a triangle ABC with sides AB = 6cm,
AC = 4cm and BC = 5cm?
Let’s start with AB.
A
6cm
B
Can you see a problem with now drawing AC ?
Ans: We don’t know what angle AC makes with AB.
We have the same problem if we try to draw BC.
Could you draw a triangle ABC with sides AB = 6cm,
AC = 4cm and BC = 5cm?
Let’s start with AB.
A
AC could be here
. . . or here . . .
or here . . .
4 cm
C
B
6cm
4cm
4 cm
4 cm
C
C
C
5cm
arc, radius 4 cm,
arc, radius 5 cm,
We need
C to be
centred
at in
A the position that makes
centred at B
BC = 5 cm.
To draw
theistriangle
accurately
we always use
There
only one
possible triangle.
compasses and draw arcs from A and B.
Could you draw a triangle ABC with sides AB = 6cm,
AC = 4cm and BC = 5cm?
A
B
6cm
4cm
5cm
C
An accurate drawing is often called a construction.
We must always show construction lines clearly.
There is only one size and shape of triangle we
can draw if we are given the lengths of 3 sides.
Tip: We can remember this as SSS ( 3 sides ).
It doesn’t matter which way up, or which side we
start with, all the triangles are congruent.
6cm
6cm
6cm
4cm
5cm
4cm
5cm
5cm
4cm
4cm
5cm
6cm
6cm
5cm
5cm
4cm
5cm
4cm
6cm
4cm
6cm
If we are given one side of an equilateral triangle we
can construct the triangle using compasses and a
straight edge instead of a ruler .
e.g. Complete the equilateral triangle ABC that has AB
as one side.
A
B
C
arc, radius AB,
arc, radius AB,
Decide
with
your
partner
how
to
complete
triangle.
Ans: We can use compasses opened
to thethe
length
AB
centred at A
centred at B
and draw arcs at A and B which will meet at C.
Now join AC and BC.
SUMMARY
 Only 1 shape and size of triangle can be drawn if
we are given the lengths of 3 sides (SSS).
 The triangle can be drawn accurately with a ruler
and compasses.
e.g. Construct a triangle with sides of lengths
6 cm, 4 cm and 5 cm.
A
B
6cm
5cm
4cm
arc, radius 4 cm,
centred at A
C
arc, radius 5 cm,
centred at B
 An accurate drawing cannot be made without
compasses.
cont.
SUMMARY
 We can construct an equilateral triangle ABC, if
AB is already drawn, using only a straight edge
and compasses.
e.g.
A
B
arcs of radius AB,
centred at A and B.
C
 If a side of the triangle is not drawn for us, we
need a ruler to draw the 1st side.
EXERCISE
1. Using a ruler and compasses only, construct
a triangle PQR with sides PQ = 8cm, PR = 6cm
and QR = 6cm.
Measure angles Q and R.
Solution:
All construction lines must be clearly shown.
8cm
P
6cm
Q
6cm
R

Q = 48

R = 84
EXERCISE
2(a) Using a ruler and compasses only, construct
an equilateral triangle with sides of length 7 cm.
(b) Measure the angles with a protractor.
Solution:
All construction
lines must be clearly shown.
7cm
P
Q
60
60
7cm
7cm
60
R
If you have been
accurate, all the
angles will be 60.