Construction using compasses
Construction using compasses works because all the points
on the radius of a circle are exactly the same distance away
from the centre of the circle.
.A
Point B is exactly
the same distance away
from the centre of the
circle as Point A.
x
.B
Equidistant means:
The same distance from
So: A and B are equidistant from X
an Arc is a part of a circle
circumference.
So: the circumference segment
AB is an arc.
Construction using compasses
This means that for 2 circles that overlap – if the circles are
the same size, the points where they cross are the equidistant
from the circle centres
Point A is equidistant from the centres
of both circles
A
.
x
x
.
B
Point B is also equidistant from the centres
of both circles
Construction using compasses
Constructing the bisector of a straight line segment.
Bisector
Bisector
means cutting the straight line in two
two
section
equally sized sections
Keeping
same
Place
Set your
thethe
point
compasses
of radius,
your
to a put
radius
Draw
the
line
segment
AB
C
the
point
of at
your
compasses
compasses
that
is more
than
point
half
A and
draw
making
sure
that
itthe
has
on
B above
and
2below
more
arcs
arcs
length
the
andline
segment
the
twoofdraw
very
distinct
endsto
cross
the two already drawn
line segment
X
A
B
at points C and D
N.B you must always
Show the construction arcs
D
Now draw a straight line from C to D.
The line crosses AB at X which is the mid-point of AB
The line CD is the perpendicular bisector of AB
Construction using compasses
Constructing the bisector of an angle.
Bisect angle BAC N.B. The vertex of the angle is always the middle letter
Put
of of
thethe
compasses
on
Setthe
thepoint
radius
compasses
Xto&about
Y in turn
half and
waydraw
alongarcs
the that
lines
intersect at Z
Put the point of the compasses on
B
X
point A and draw two arcs to cut
Z AB and AC
A
Y
C
This identifies two points X & Y
equidistant
A
N.B youfrom
mustpoint
always
Show the construction arcs
Draw a line from A to Z – this is the bisector of the angle
This works for any kind of angle acute, obtuse or reflex
Construction using compasses
Constructing a perpendicular from a point P on a line segment.
C
A
B
P
Put
the
compasses
Set the
the
radius
the
compassesonto
Join
CP.point
CP isofof
the
perpendicular
tobe
thelarger
original
P,
draw
cut the
line
with2 aarcs
90otoangle
at Pline
segment at A and B
Put Notice
the point
A and
B inAturn
drawbeen
arcs
thatononce
points
andand
B have
thatfound
intersect
C
the at
construction
is identical to finding
the perpendicular bisector of the line. Why?
Construction using compasses
Constructing a perpendicular from a point P onto a line segment.
Now the
construct
thethe
perpendicular
With
point of
compasses on P,
bisector
asarcs
before
draw two
that intersect the line
P
at A and B
B
A
Put the point on A and B in turn
and draw arcs that intersect at C
C
Join CP. CP is the perpendicular to the original
line with a 90o angle at P
Construction using compasses
Constructing an angle of 60o.
R
P
60o
Because
the same
radius was used
Join
the points
together
P, R and
Q are
What
shape
do all
youequidistant
draw?
from each other.
Equilateral triangle
The internal angles
in an equilateral triangle are
all 60o
Q
Draw a large arc that intersects the line at Q
Keeping the radius the same and draw an arc from Q that intersects
at P and crosses the other arc