Constructions: Congruent Segments and Perpendicular Bisector of a Segment
In geometry, constructions utilize two tools:
A compass: An instrument with two arms, one sharp and one with a pencil that
can be used to draw circles or arcs.
A Straight Edge: An unmarked ruler that can be used to draw straight lines.
Constructing Congruent Segments (Copying a Segment):
Given: AB (Line segment).
Task: To construct a line segment congruent to AB (line segment).
Instructions:
1) If a reference line does not already exist, draw a reference line with your straightedge
upon which you will make your construction. Place a starting point on the reference
line.
2) Place the point of the compass on point A.
3) Stretch the compass so that the pencil is exactly on B.
4) Without changing the span of the compass, place the compass point on the starting
point on the reference line and swing the pencil so that it crosses the reference line.
Label your copy if necessary.
(Result: Your copy and (line segment) AB are congruent)
1) In the box to the right, construct a line
segment congruent to AB and label it
XY on the given line.
A
B
2) Using only a straight edge and a
compass, construct a line segment
congruent to MT in the box to the right.
M
T
3) Given: AB
Construct: AB  CD in the box to the
right.
A
B
4) In the box to the right, constructs a line
segment congruent to EL in the box to
the right.
E
L
5) Given ABC shown below, using only
a compass and a straight edge, constrict
a line segment congruent to CB in the
box to the right and label it XY
B
A
C
6) Given: EML
Construct: EL  XY in the box to the
right.
M
E
L
Constructing a Perpendicular Bisector (Bisecting a Line Segment):
Given: AB (Line segment).
Task: Draw a perpendicular bisector of AB (line segment).
Instructions:
1) Place your compass point on A and stretch the compass MORE THAN half way to
point B, but not beyond B.
2) With this length, swing a large arc that will go BOTH above and below AB .
(If you do not wish to make one large continuous arc, you may simply place one
small arc above AB and one small arc below AB .)
3) Without changing the span on the compass, place the compass point on B and swing
the arc again. The two arcs you have created should intersect.
4) With your straightedge, connect the two points of intersection.
5) This new straight line bisects AB . Label the line and point of intersection if
necessary.
(Result: Created line is perpendicular to AB , M is the midpoint of AB and MA  MB )
1) Using only a compass and a straight
edge, construct a perpendicular bisector
of AB and label it c.
2) Given: MT
Construct: A perpendicular bisector of
MT , label it f.
M
A
T
B
3) Given: AB .
Construct: CD  AB and bisecting AB .
4) Using only a compass and a straight
edge, construct a perpendicular bisector
of XY .
Y
B
X
A
5) On ABC shown below, construct the
perpendicular bisector of BC and label
it l.
6) Given: XYZ
Construct: A perpendicular bisector of
YZ .
X
B
Y
A
Z
C