2.2 Angle Bisectors
Goal
Bisect an angle.
VOCABULARY
Angle bisector An angle bisector is a ray that divides an
angle into two angles that are congruent.
Example 1
Find Angle Measures
BD
&*( bisects aABC, and maABC 110.
Find maABD and maDBC.
A
D
Solution
110
BD
&*( bisects aABC, so maABD is half of
maABC.
1
maABD p maABC
2
B
C
1
p 110
2
55
Answer maDBC maABD 55
Checkpoint HK
&*( bisects aGHJ. Find maGHK and maKHJ.
1.
2.
G
K
3.
G
J
32
J
K
K
J
H
161
H
G
H
maGHK 16;
maKHJ 16
maGHK 45;
maKHJ 45
maGHK 80.5;
maKHJ 80.5
Lesson 2.2 • Geometry, Concepts and Skills Notetaking Guide
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Angle Measures and Classification
Example 2
MO
&
&( bisects aLMN, and maLMO 46.
L
O
a. Find maOMN and maLMN.
b. Determine whether aLMN is acute, right,
obtuse, or straight. Explain.
46
M
N
Solution
a. MO
&
&( bisects aLMN, so maLMO maOMN.
maOMN maLMO 46
The measure of aLMN is twice the measure of aLMO.
maLMN 2 • maLMO 2 • 46 92
b. aLMN is obtuse because its measure is between 90 and 180.
Checkpoint QS
&*( bisects aPQR. Find maSQP and maPQR. Then
tell whether aPQR is acute, right, obtuse, or straight.
4.
5.
R
29
S
S
P
6.
P
S
60
P
45
Q
maSQP 29;
maPQR 58;
acute
32
R
Q
maSQP 45;
maPQR 90;
right
Geometry, Concepts and Skills Notetaking Guide • Chapter 2
R
Q
maSQP 60;
maPQR 120;
obtuse
Use Algebra with Angle Measures
Example 3
RQ
&*( bisects aPRS. Find the value of x.
Q
(6x 1)
Solution
maPRQ maQRS
( 6x 1 ) 85
6x 1 1 85 1
P
85
R
S
RQ
&*( bisects aPRS.
Substitute the given angle measures.
Subtract 1 from each side.
6x 84
6x
84
6
6
Simplify.
x 14
Simplify.
Divide each side by 6 .
Follow-Up Check your answer for Example 3.
Substitute your value of x in the original equation to determine
whether it is a solution.
(6x 1) ⱨ 85, (6(14) 1) ⱨ 85, (84 1) ⱨ 85, 85 85
Checkpoint BD
&*( bisects aABC. Find the value of x.
7.
8.
C
D
A
D
9x
(8x 3)
55
(x 12)
A
43
B
B
C
3
Lesson 2.2 • Geometry, Concepts and Skills Notetaking Guide
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