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Geometry A
Chapter 4 Review
Name _________________________________
Date ___________________
Hour ______
CHAPTER 4 REVIEW
For numbers, 1 through 7, classify the triangle by its side lengths or angles.
1. no congruent sides
2. two sides congruent
3. Angles measures: 25°, 130°, 25°
4. Angles measures: 60°, 60°, 60°
5. Side lengths: 10cm, 10cm, 10cm
6. Side lengths: 3m, 4m, 5m
B
7. In ABC, AB = 4x – 1, BC = x + 5, and AC = 7. Also, AB  BC .
A
C
Given, ABC  DEF. Complete the statement.
8. EF  ____
9.. A  ___
10. E  ____
11. mC = ____
12. AC = ____
13. CBA  ____
Write the correct congruence statement for these triangles.
14.  ______   _______
Find the value of x.
15.
16.
4x°
5x°
17.
Using the diagrams choose the appropriate postulate or theorem that proves triangles congruence’s:
A. SAS
B. SSS
C. ASA
D. AAS
E. HL
If not, write not enough info.
18.
19.
20.
21.
22.
23.
24.
25.
26.
C
27.
A
28.
E
F
G
29.
J
K
M
L
B
H
D
O
30.
W
X
Q
R
Z
V
U
31.
32.
P
S
A
Y
P
T
Q
33. Proof
Given: ST  UT , SV  UV
Prove: TSV  TUV
Statements
Reasons
1. ST  UT , SV  UV
1.
2. TV  TV
2.
3. TSV  TUV
3.
4. TSV  TUV
34. Proof
4.
Given: WZ XY ,WZ  XY
Prove: XWZ  ZYX
Statements
Reasons
1. WZ XY ,WZ  XY
1.
2.
2. XZ  XZ
3. WZX  YXZ
4. XWZ  ZYX
35. Proof
3.
4.
Given: VU  UW , XW  UW ,VW  XU
Prove: VUW  XWU
Statements
Reasons
1. VU  UW , XW  UW ,VW  XU
1.
2. UW  UW
2.
3. VUW and XWU are right
angles
3.
4. VUW  XWU
4.
Find the value of x for problems #36 – 44.
36.
37.
38.
70
54°
x°
39.
x
x°
40°
40.
41.
x°
x°
(5x – 6)°
(3x + 10)°
x°
x°
10
42.
43.
44.
x°
(3x + 10)°
2x°
(5x – 10)°
75°
3x°
55°
4x°
45. In ABC, if AB  BC and mC = 50°, then find the measure of mA = _________.
46. In ABC, if AB  BC , AB = 6x + 9 and BC = x + 29, then find x = _________.
47. In ABC, if AB  BC , AB is three times the length of AC, then find the length of AB if the perimeter of
the triangle is 49. AB = _________.
48. Find the measure of B.
49. Find the measure of DBC
B
D
52°
A
48°
C
A
B
C
50. Find the value of x.
51. Find the value of x.
52. Find the value of x.
2x°
3x°
55°
53. In ABC, ACB  CAB; CB = 9x – 8; AB = 4x + 12; AC = 20. Find AB.
B
A
C
54. In CAT, CT = AT. The length of CT is three times the length of CA . Find the length of CT if the
perimeter of the triangle is 54 inches.
55. In SAT, if SA  AT and mS = 44°, then find the mT.
56. What is the measure of each base angle of an isosceles triangle if its vertex angle measures 30 degrees and
its 2 congruent sides measure 29 units?
30°
29
29