Constructions: Congruent Angles and Bisector of an Angle
Constructing Congruent Angles (Copying an Angle):
Given:

BAC (Angle).
Task: To construct an angle congruent to

BAC (Angle).
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 the vertex of

BAC (point A ).
3) Stretch the compass to any length so long as it stays ON the angle.
4) Swing an arc with the pencil that crosses both sides of

BAC .
5) Without changing the span of the compass, place the compass point on the starting point of the reference line and swing an arc that will intersect the reference line and go above the reference line.
6) Go back to

BAC and measure the width (span) of the arc from where it crosses one side of the angle to where it crosses the other side of the angle.
7) With this width, place the compass point on the reference line where your new arc crosses the reference line and mark off this width on your new arc.
8) Connect this new intersection point to the starting point on the reference line. Label your copy if necessary.
(Result: Your new angle is congruent to

BAC )

1) Using only a straight edge and a
compass, construct an angle
congruent to

ABC in the box to the
right, on the given line, and label it

XYZ .
B
A C
2) Given:

MTV
Construct:

MTV
 
JEC
to the right.
in the box
M
T V
3) In the box to the right, constructs an
angle congruent to

PET in the box to
the right.
T
E P

4) Given:

XYZ
Construct:

DOG
 
XYZ in the box
to the right.
Z
X Y
5) Given

ABC shown below, using only
a compass and a straight edge, constrict
an angle congruent to

ABC

in the
box to the right and label it XYZ
A
B
C
6) Given:

CAT
Construct:

XYZ
 
ACT
to the right.
in the box
A
C
T

Constructing an Angle Bisector (Bisecting an Angle):
Given:

BAC (Angle).
Task: To bisect

BAC (Angle).
Instructions:
1) Place the point of the compass on the vertex of

BAC (point A ).
2) Stretch the compass to any length so long as it stays ON the angle.
3) Swing an arc so the pencil crosses BOTH sides of

BAC .
4) Place the compass point on one of these new intersection points on the sides of

BAC .
5) Without changing the width of the compass , place the point of the compass on the other intersection point on the side of the angle and make the same arc. Your two small arcs in the interior of the angle should be crossing.
6) Connect the point where the two small arcs cross to the vertex A of the angle. Label the line if necessary
(Result: You created two new angles that are of equal measure and are each 1/2 the measure of

BAC )

1) Using only a compass and a straight
edge, construct an bisector
of

BAC and label it AX .
B
A C
3) Given:

EML .
Construct: An angle bisector of

EML .
E
L
M
2) Given:

XYZ
Construct: An angle bisector of

XYZ .
X Z
Y
4) Using only a compass and a straight
edge, construct the angle bisector
of

DOG and label it OX .
D
O G

5) On

EML shown below, construct the
angle bisector of

EML
E
M
L
6) Given:

XYZ
Y
Construct: XQ An angle bisector of

YXZ .
X
Z