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

Name: _______________________________
Period: ______
Geometry Chapter 4 Test – Version A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
A
1. In the triangles below (∆ABC and ∆FED), find m
B
E
D
C
, given
,
, and m
F
a. m
b. m
c. m
d. m
____ 2. 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
=
=
____ 3. Given:
Identify all pairs of congruent corresponding parts.
A
M
B
a.
b.
c.
d.
C
,
,
,
,
O
N
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
.
____
4. What additional information do you need to prove
by the SAS Postulate?
a.
b.
C
B
c.
d.
D
A
____
5. Given the lengths marked on the figure and that
bisects
, use SSS to explain why
.
4 cm
E
A
3 cm
3 cm
D
4 cm
C
B
a.
b.
c. The triangles are not congruent.
d.
____
6. Daphne folded a triangular sheet of paper into the shape shown. Find
, and m
.
a.
b.
E
=
=
c.
d.
, given
,
=
=
D
C
A
42º
61º
____
22º
7.
B
Determine if you can use ASA to prove
. Explain.
E
a.
A
B
||
C
||
D
is given.
because both are right angles. By the Vertical
Angles Theorem,
. Therefore,
by SAS.
b.
is given.
because both are right angles. No other
congruence relationships can be determined, so ASA cannot be applied.
c.
is given.
because both are right angles. By the Adjacent
Angles Theorem,
. Therefore,
by ASA.
d.
is given.
because both are right angles. By the Vertical
Angles Theorem,
. Therefore,
by ASA.
____ 8.
supports it.
For these triangles, select the triangle congruence statement and the postulate or theorem that
L
a.
b.
J
, SAS
, HL
c.
d.
, SAS
, HL
K
B
A
C
____
9.
Find the measure of each numbered angle.
>
|
|
3 1

117
a.
b.
c.
d.
2
m
m
m
m
=
=
=
=
>
,m
,m
,m
,m
=
=
=
=
,m
,m
,m
,m
=
=
=
=
____ 10.
One of the acute angles in a right triangle has a measure of
acute angle?
a.
c.
b.
d.
____
11.
Classify
by its angle measures, given m
,m
. What is the measure of the other
, and m
.
D
25º
60º
A
75º
B
a. right triangle
b. equiangular triangle
C
c. acute triangle
d. obtuse triangle
12. Find the value of x if the triangle is an equiangular, equilateral triangle.
(3x + 6) o
13.
An isosceles triangle has a perimeter of 54 cm. The congruent sides measure (2x + 3) cm. The length of
the third side is 4x cm. What is the value of x?
Given: CBA  CDA ,
14.
bisects
Prove:
B
C
A
D
Complete the proof.
Statements
1. CBA  CDA,
bisects
Reasons
1. Given
2. BAC  DAC
2.
3.
3. Reflexive Property of Congruence
4.
4.
5.
5.
Find
15.
.
is an isosceles triangle.
is the longest side with length
.
=
and
=
7 x+ 3
A
B
2 x +8
3 x+ 6
C
5
2x
+
3x
1
16. What congruence postulate proves that these triangles are congruent? Then, find the value of x.
.
17.
Given: P is the midpoint of
Prove:
T
and
.
R
P
S
Q
Complete the proof.
Proof:
Statements
1. P is the midpoint of
2.
Reasons
and
1. Given
.
2.
,
3.
3. Vertical Angles Theorem
4.
4.
18. Show
for
6a - 2
A
.
D
a+7
4a - 2
B
C
16
19. 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
3.

Reasons
1. Given
2.
3. Right Angle Congruence Theorem
4. ST  UT
4.
5. RT  RT
5.
6.
6.
.
20.
Find
.
(
L
(4x + 7)º
(6x - 9)º
118º
K
M
21.
N
Given that
and m
= 34º, find m
.
E
34º
A
D
C
B
22.
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:
1.
2.
3.
,
Statements
,
Reasons
1. Given
2. Given
3.
4.
4.
5.
5. Definition of congruent triangles
Name: _______________________________
Period: ______
Geometry Chapter 4 Test Answer Sheet
VERSION: A
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.
Statements
1. CBA  CDA,
bisects
1. Given
Reasons
2. BAC  DAC
2.
3.
3. Reflexive Property of Congruence
4.
4.
5.
5.
15. AB = __________
16. Congruence postulate: ___________
x = ______
17.
Statements
1. P is the midpoint of
2.
and
Reasons
.
1. Given
2.
,
3.
3. Vertical Angles Theorem
4.
4.
18.
19.
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.
20.
. = ________
21. m
.= __________
22.
1.
2.
3.
,
Statements
,
Reasons
1. Given
2. Given
3.
4.
4.
5.
5. Definition of congruent triangles