Name:_________________________
Angle/Segment Bisectors
Date:_____ Period:____
Ms. Anderle
Angle/Segment Bisectors:
An angle bisector is a ray, line segment, or line that divides an angle into two
congruent adjacent angles. An angle has exactly one bisector.
If BD is the bisector of ABC , then:
 mABD  mCBD or ABD  CBD
1
 m ABD  m ABC
2
1
 m CBD  m ABC
2
Example 1:
If the mABC  50 and BD bisects ABC , what is the measure of ABD ?
A segment bisector divides a segment into two congruent segments. In addition, a
segment bisector passes through the midpoint of that segment. Therefore, a
midpoint also divides a segment into two congruent segments.
Example 2:
The length of line segment AB is 8 inches. Segment PM bisects segment AB. In
inches, what is the measure of AM and BM?
Examples:
Complete all work on a separate sheet of paper. Show all work, including diagrams.
1. Ray PQ bisects HPJ . If m QPJ  2x  9 and m QPH  x  29 , what is
the measure of HPJ ?
2. Point R is the midpoint of XY . If XR = 3n+1 and YR = 16 – 2n, what is the
length of XY?
3. Segment WX bisects line segment AB. If AX = 5n – 8 and BX = 2n + 19, then
what is length of AB?
4. Ray AC bisects BAD . If mBAC  3x  5 and mCAD  6x  7 , what is
the value of x and the measure of BAC ?
5. Ray QN bisects PNM . If mPNQ  4x  8 and m MNQ  3x  5 , what is
the measure of PNM ?
6. Point L is the midpoint of RP . If RL = 15x and LP = 5(x + 6), what is the
length of RP?
7. Segment QW bisects line segment ZY. The length of QW = 60x and the
length of WY = 4(5x + 20). Find the length of QY.
8. Segment BX bisects WXY . If the mWXB  70  2x and the
m YXB  2  x  5  , what is the measure of WXY ?
9. Point K is the midpoint of TJ . The length of TK = 3w + 11 and the length of
JK = 18 – 4x. What is the length of TJ?
10. Ray BA bisects WAY . The mWXB  5x  13 and mYXB  43  2x .
What is the measure of WAY ?
11. Ray BA bisects WAY . The mWAY  2y and mYAB  9y  56 . What is
the measure of WAB ?