Transcript Basic Geometric Constructions

Basic Geometric
Constructions
By: Mr. Erlin
Geometry 1
Tamalpais High School
Copy a Segment
1) Since a segment is a part of a
line, we’ll start by drawing a
ray that is somewhat longer
than our intended segment,
and call the starting point A’.
2) Place the Needle end of the
compass on point A, and
adjust its length to match the
distance AB.
3) Without changing the width of
the compass, put the Needle
end of the compass on point
A’, and draw the arc to cross
your ray. Label the point of
intersection B’. You’ve just
copied AB to A’B’
A
A’
B
B’
Copy An Angle
4) Now go back to the original
1) Since an angle is two rays with
angle, and put your needle on
a common vertex we’ll start by
the point of intersection of AB
drawing a ray and call ray
and the arc. Measure the
B’A’.
distance along the arc to the
ray BC.
2) Place
the Needle end of the
5) Without
width of
compasschanging
on point the
B, and
the
compass,
put crosses
your needle
make
an arc that
over
on
theBA
point
of intersection of
from
to BC.
the arc and B’A’. Make an arc
3) Without
changing
thearc
width
that crosses
the first
youof
the
put angle.
the Needle
drewcompass,
on this new
6) Draw
raycompass
from B’ thru
the
end ofathe
on point
point
of draw
intersection
the two
B’, and
the arcofcrossing
arcs.
Label
a pointtoon
the than
ray
B’A’ long
enough
more
as
C’. where
You’veB’C’
copied
cross
will the
be. angle
ABC as A’B’C’.
C
B
A
C’
B’
A’
Bisecting a Segment
1) Place the needle of your compass on A.
Make its width more than half-way to B,
and make a half-circle.
2) Without changing the width of the
compass, put the needle of your
compass on B. Make a half-circle that
overlaps the first one.
3) Draw a line that connects the two points
of intersection of the two half-circles.
That new line is both a bisector of the
segment AB, and is perpendicular to
AB.
A
B
Bisecting an Angle
C
1) Place the needle of your compass on B.
Draw an arc that crosses both BA and
BC.
2) Label the intersection of the arc and BA
“D”, and the intersection of the arc and
BC “E”.
3) Place the needle of the compass on D,
and set the width to match more than half B
the distance to E. Make a half-circle.
4) Leave the compass width as it is. Place
the needle of the compass on E, and
make a half-circle overlapping the
previous half-circle.
5) Draw a line that connects the two points
of intersection of the two half-circles.
That new line is both a bisector of the
angle ABC.
E
D
A