© Glencoe/McGraw-Hill
6–3
NAME
DATE
PERIOD
Study Guide
Angle Bisectors of Triangles
NAME
6–3
DATE
PERIOD
Skills Practice
Angle Bisectors of Triangles
An angle bisector of a triangle is a segment that bisects an angle
of the triangle and has one endpoint at the vertex of that angle and
the other endpoint on the side opposite that vertex.
In ACD, D
wB
ww bisects /ADC, and C
wE
ww bisects /ACD.
1. If m1 40, what is m2? 40
A
E
2. Find mACD if m4
Example:
50
25.
D
3. What is m3 if mACD
B
1
2
18
36?
3
4. If m1
5. What is mDCA if mDCE
wV
w is an angle bisector of RST.
R
6. Find mADB if mBDC
39.
39
7. What is mACD if m4
18?
36
8. Find m2 if m1
2. m 2
________
9. If m3
m/1
20?
43.
43
21
21, what is m4?
CAE. A
wD
w
24
In MOR, M
wP
w bisects /OMR, R
wN
w bisects /MRO, and O
wS
w bisects /MOR.
11. Find m6 if mMOR
4. ________ bisects
24?
ACE. C
wF
w
12. What is mOMR if m1
O
17
34.
23?
N
46
M
5. m 6
________(m CEA)
Geometry: Concepts and Applications
6. m ACE
________(m 3)
13. If m3
1
!!
2
55, what is m4?
1
2
S
15. Find m1 if m2
2
16. If m4
7. Draw and label a figure to illustrate this situation. H
wS
w is an
angle bisector of GHI, and S is between G and I.
A sample answer is given.
27.
233
Geometry: Concepts and Applications
32?
P
34
R
120
60, what is mMRO?
17. What is mSOR if m6
18. If mMRP
16
5
27
15?
15
112, what is m3?
19. Find mOMP if mPMR
© Glencoe/McGraw-Hill
55
14. What is mMOS if mMOR
6
30.
56
30
20. What is m4 if MRO is a right angle?
45
© Glencoe/McGraw-Hill
234
Geometry: Concepts and Applications
(Lesson 6-3)
A7
10. What is mECD if mECA
3. ________ bisects
C
40
Answers
In ACE, C
wF
w, w
EB
w, and A
wD
w are angle bisectors.
1. m 3 ________ m/4
4
45, what is mADC? 90
© Glencoe/McGraw-Hill
6–3
NAME
DATE
PERIOD
6–3
Practice
Angle Bisectors of Triangles

In DEF, DH bisects
1. If m 2
EFD.
PERIOD
Reading to Learn Mathematics
Key Terms
36, what is m EDF? 72
angle bisector of a triangle a segment that separates an angle
of the triangle into two congruent angles; one of the
endpoints of an angle bisector is a vertex of the triangle, and
the other endpoint is on the side opposite that vertex
34
68.
DATE
Angle Bisectors of Triangles

EDF, and FG bisects
2. Find m 4 if m EFD
NAME
Reading the Lesson
3. What is m EDF if m 1

In LMN, LP bisects
bisects MNL.

NLM, MQ bisects
Median; the segment passes through a
vertex and the midpoint of the side opposite
the vertex.
b. C
wD
w Altitude; the segment passes through a
A
vertex and is perpendicular to the side
opposite the vertex.
c. w
CH
w None of these; the segment passes through
a vertex of the triangle but does not intersect
the opposite side, nor does it bisect an angle.
d. w
BG
w Angle bisector; the segment separates an
angle of the triangle into two congruent angles.

LMN, NR
57.5
115.
18, what is m 3? 18
7. What is m 1 if m NLM
Geometry: Concepts and Applications
8. Find m LNM if m 5
48?
63.
G
F
H
E
D
B
2. Complete each sentence with one or two words to form a statement that is always true.
a. A(n) median passes through a vertex of a triangle and through the midpoint of the
opposite side.
b. A(n) perpendicular bisector of a triangle passes through the midpoint of a side
of a triangle and is perpendicular to that side of the triangle.
c. A(n) altitude of a triangle passes through a vertex of a triangle and is perpendicular
to the side of the triangle opposite that vertex.
d. A(n) angle bisector of a triangle is a segment that bisects an angle of the triangle.
e. Every triangle has 3 angle bisectors.
f. You can use a compass and straightedge to construct the angle bisectors of a
triangle.
24
126
9. Find m ABC if w
BD
w is an angle bisector of ABC. 30
m ABC
C
Helping You Remember
(4x # 6)°
3. Write several sentences comparing a median, an angle bisector, a perpendicular bisector,
and an altitude of a triangle. Be sure to tell some characteristics shared by two or more
of the segments. Sample answer: A median, an angle bisector, and
an altitude all have one vertex as an endpoint. A median and a
perpendicular bisector both have one endpoint as a midpoint of a
side of the triangle. An altitude and a perpendicular bisector are both
perpendicular to a side of the triangle. A median and an angle
bisector split some part of the triangle into two congruent parts.
© Glencoe/McGraw-Hill
235
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
236
Geometry: Concepts and Applications
(Lesson 6-3)
A8
5. Find m 6 if m MNL
6. If m 4
a. C
wE
w
23, what is m 3? 23
Answers
4. If m 4
1. In the figure, E is the midpoint of A
wB
w, F is the midpoint of w
BC
w, and CBA is bisected by
BG
w
w. For each segment, write the term that best describes it from this list: median, angle
bisector, perpendicular bisector, or altitude. Explain your choice. If the segment cannot be
described using one of these terms, explain why.
54
27?