Download Name: Period: ______ Geometry Chapter 4 Test – Version B

Name: _______________________________
Period: ______
Geometry Chapter 4 Test – Version B
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Two Seyfert galaxies, BW Tauri and M77, represented by points A and B, are the same distance
from Earth, represented by point C (so CA = CB). What is m ?
C
115°
A
a. m
b. m
____
B
D
=
=
c. m
d. m
=
=
2. Daphne folded a triangular sheet of paper into the shape shown. Find
, and m
.
, given
E
D
C
42º
61º
A
22º
a.
b.
=
=
c.
d.
3. Given the lengths marked on the figure and that
.
=
=
bisects
, use SSS to explain why
4 cm
E
A
3 cm
3 cm
D
C
4 cm
____
B
B
a.
b.
c.
d. The triangles are not congruent.
,
____
4. For these triangles, select the triangle congruence statement and the postulate or theorem that
supports it.
L
J
K
B
A
C
a.
b.
____
, HL
, HL
c.
d.
5. Determine if you can use ASA to prove
, SAS
, SAS
. Explain.
E
A
C
||
||
D
B
a.
is given.
because both are right angles. No other
congruence relationships can be determined, so ASA cannot be applied.
b.
is given.
because both are right angles. By the Adjacent
Angles Theorem,
. Therefore,
by ASA.
c.
is given.
because both are right angles. By the Vertical
Angles Theorem,
. Therefore,
by ASA.
d.
is given.
because both are right angles. By the Vertical
Angles Theorem,
. Therefore,
by SAS.
6. Find the measure of each numbered angle.
>
|
3 1
|
____

117
a.
b.
c.
d.
m
m
m
m
2
=
=
=
=
>
,m
,m
,m
,m
=
=
=
=
,m
,m
,m
,m
=
=
=
=
____
7. One of the acute angles in a right triangle has a measure of
acute angle?
a.
c.
b.
d.
. What is the measure of the other
____
8. What additional information do you need to prove
by the SAS Postulate?
C
B
D
A
a.
b.
____
c.
d.
9. In the triangles below (∆ABC and ∆FED), find m
m
.
A
B
E
D
C
, given
,
, and
F
a. m
b. m
c. m
d. m
____ 10. Classify
by its angle measures, given m
,m
, and m
.
D
25º
60º
75º
A
B
C
a. obtuse triangle
b. acute triangle
c. right triangle
d. equiangular triangle
____ 11. Given:
Identify all pairs of congruent corresponding parts.
A
M
a.
b.
c.
d.
B
C
O
N
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
12. Find the value of x if the triangle is an equiangular, equilateral triangle.
(4x + 8) o
13. An isosceles triangle has a perimeter of 76 in. The congruent sides measure (3x + 3) cm. The
length of the third side is 4x cm. What is the value of x?
14.
=
is an isosceles triangle.
is the base with length
and
=
. Find
.
.
4 x+ 4
A
B
7 x +8
8 x+ 3
15. Find
(
L
.
C
(4x + 7)º
(6x - 9)º
118º
K
M
N
16. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles.
Given:
,
,
,
Prove:
B
D
C
A
E
Complete the proof.
Proof:
Statements
1.
,
,
2.
3.
1. Given
2. Given
3.
4.
4.
5.
5. Definition of congruent triangles
Reasons
17. The figure shows part of the roof structure of a house. Use SAS to explain why
R
||
S
||
T
U
Statements
1. RT  SU, T is the midpoint of SU
2.
and
are right angles
Reasons
1. Given
2.

3.
3. Right Angle Congruence Theorem
4. ST  UT
4.
5. RT  RT
5.
6.
6.
18. Given: P is the midpoint of
Prove:
and
T
.
R
P
S
Q
Complete the proof.
Proof:
Statements
1. P is the midpoint of
and
2.
Reasons
1. Given
.
2.
,
3.
3. Vertical Angles Theorem
4.
4.
19. Show
for
.
6a - 2
A
D
a+7
B
4a - 2
16
C
.
5
2x
3x
+1
20. What congruence postulate proves that these triangles are congruent? Then, find the value of x.
21. Given: CBA  CDA ,
bisects
Prove:
B
C
A
D
Complete the proof.
Statements
1. CBA  CDA,
bisects
1. Given
2. BAC  DAC
2.
3.
3. Reflexive Property of Congruence
4.
4.
5.
5.
22. Given that
and m
E
23º
A
D
C
B
Reasons
= 23º, find m
.
Name: _______________________________
Period: ______
Geometry Chapter 4 Test Answer Sheet
VERSION: B
TEST NUMBER: ____
For #1 – 11, write the LETTER of your answer choice only.
1.
7.
2.
8.
3.
9.
4.
10.
5.
11.
6.
12. x = ______
13. x = ______
14. AB = __________
15.
. = ________
16.
1.
2.
3.
,
Statements
,
Reasons
1. Given
2. Given
3.
4.
4.
5.
5. Definition of congruent triangles
17.
Statements
1. RT  SU, T is the midpoint of SU
2.
and
are right angles
3.

Reasons
1. Given
2.
3. Right Angle Congruence Theorem
4. ST  UT
4.
5. RT  RT
5.
6.
6.
18.
Statements
1. P is the midpoint of
and
2.
Reasons
.
1. Given
2.
,
3.
3. Vertical Angles Theorem
4.
4.
19.
20. Congruence postulate: ___________
x = ______
21.
22. m
Statements
1. CBA  CDA,
bisects
1. Given
2. BAC  DAC
2.
3.
3. Reflexive Property of Congruence
4.
4.
5.
5.
.= __________
Reasons