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Name ______________________________________ Date _____________________
Geometry A Chapter 4 Test Review
Part I: Classify each of the triangles. Use two words from the following list. Choose
one to describe the angles and one to describe the sides.
ACUTE, ISOSCELES, EQUILATERAL, EQUIANGULAR, OBTUSE, RIGHT, SCALENE
1.
60
2.
34
30
34
Sides: __________________________
Sides: __________________________
Angles: __________________________
Angles: __________________________
4. Classify  LMN below, once
describing its sides, and once its
angles.
L
3. In the triangle below:
B
90  x
A 2x  40
5x 10
C
a. Find x. __________________
72
N
b. Find all 3 angles.
108
M
 A = ______  B = _______  C = _______
c. Classify the triangle using two words
from the list above.
Sides: _____________________
Angles: ____________________
Sides: ________________________
Angles: _______________________
In #'s 5-8, use the fact that PQRS  TUVW to give the name of the side or angle
congruent to the given one.
5.  U  ________
6. SP  _________
7.  QRS = ________
Use the fact that  XYZ   ABC
to find the following angle and side
measures.
C
Y
70
X
Use the fact that  STU   WVB
to find the values of the variables
and measures of angles.
A
T
88
10
12
S
3y + 1
y
2y + 6
7
W
8x 12
3x
U
V
B
Z
B
8. XY = _______
11. x = _________
9.  Z = _______
12. y = __________
10.  ABC = _______
13.  U = _________
4x  3
In #'s 14-19, find the side lengths, angles and variables indicated.
14.
G
15.
B
A
L 68
 LGB = 110
 A = _______________
 B = __________________
16. C
17.
F
4x + 20
6x
y
132
D
G
8x
x = ________ CD = _________
y = _________  EFG = __________
18
E
18.
F
52
19.
E
1
1
x
2
120
FE  FG
3
x
2
G
 1 = _________  2 = ____________
8x 
20.
x = _________  3 = __________
21.
2
3x  2 y
3x
30x  20
x  12 y 
x = ___________
4 x  6 y
x = _________ y = ___________
In #'s 20-25, determine whether or not the triangles are congruent. If they are not, circle
NO. If they are, circle YES and give the reason (SSS, SAS, ASA, AAS or HL) and
complete the congruence statement.
G
E
A
20.
21.
B
C
D
E
T
D
F
L
Congruent?
YES or
NO
Congruent?
YES or
NO
Reason _______________
Reason _______________
 ABC   ____ ____ ____
 DEF   ____ ____ ____
S
G
22.
M
23. KL Bisects  MKP
K
H
P
J
Congruent?
L
YES or
NO
Congruent?
YES or
P
NO
Reason _______________
Reason _______________
GHJ   ____ ____ ____
 KLM   ____ ____ ____
24. PO  QR
25. U is the midpoint of SW
P
W
E
U
O
Q
R
N
S
T
Congruent?
YES or
NO
Congruent?
YES or
NO
Reason _______________
Reason _______________
 POQ   ____ ____ ____
 SUE   ____ ____ ____
Complete the proofs.
Hint: You will use SSS, SAS, ASA, AAS or HL to prove two triangles are congruent.
You will use CPCTC after this to prove other parts are congruent.
(A hint like this would not be in the directions on a test.)
26.
A
D
B
C
Given: AB || CD, BD = AC and  ABC = 90o
Prove:  ABC   DCB
1. ___________________________ 1. ____________________________
2. ___________________________ 2. ____________________________
3. __________________________
3. ____________________________
4.  ABC +  DCB = 180o
4. ___________________________
5. __________________________
5. Substitution
6.  DCB = 90o
6. Subtraction
7. ___________________________ 7. __________________________
A
8. ____________________________ 8. HL
27. Given: AB = AC, BD = CD
Prove:  B =  C
1. ______________________ 1. ____________________
2. _____________________
2. ____________________
3. _____________________ 3. ____________________
B
C
D
4. _____________________ 4. ____________________
5. ______________________ 5. ____________________