AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Using Triangle Congruence Theorems — Unit test Answers

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21
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Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?

A
SSS
B
AAS
C
SAS
D
HL
22
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The figure was created by repeatedly reflecting triangle NMP.

Question illustration
A
36 in.
B
42 in.
C
44 in.
D
48 in.
23

Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.

Question illustration
A
Yes, all the angles of each of the triangles are acute.
B
Yes, they are congruent by either ASA or AAS.
C
No, B is not congruent to Q.
Option C
D
No, the congruent sides do not correspond.
24

Which shows two triangles that are congruent by the SSS congruence theorem?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
25

Quadrilateral A B C D is rotated 145 degrees about point T to form quadrilateral A prime B prime C prime D prime.

Question illustration
A
ABCD ≅ A'B'C'D'
B
ABCD ≅ A'D'C'B'
C
CDAB ≅ A'D'C'B'
D
CDAB ≅ C'B'A'D'
26

Which of these triangle pairs can be mapped to each other using a single reflection?

Question illustration
A
Triangles F E G and F G L are congruent. Triangle F E G is reflected across line F G to form triangle F G L.
Option A
B
Triangles F E G and G L M are congruent. Triangle E F G is rotated about point G to form triangle G L M.
Option B
C
Triangles F E G and L M N are congruent. Triangle F E G is shifted down and to the right to form triangle L M N.
Option C
D
Triangles L M N and E F G are congruent. Triangle F E G is reflected across a line to form triangle L M N. Triangle L M N is also slightly higher and to the right of triangle E F G.
Option D
27

The triangles are congruent by SSS or HL.

Question illustration
t
translation only
r
rotation only
r
rotation, then reflection
r
reflection, then translation
28

Which relationships in the diagram are true? Select three options.

A
△ACF ≅ △ECF by HL
B
ΔCBF ≅ ΔCDF by SSS
C
ΔBFA ≅ ΔDFE by SAS
D
ΔCFD ≅ ΔEFD by SSS
E
ΔCBE ≅ ΔCDA by HL
29

Line segments AD and BE intersect at C, and triangles ABC and DEC are formed. They have the following characteristics: ∠ACB and ∠DCE are vertical angles∠B ≅ ∠EBC ≅ EC

A
HL
B
ASA
C
SSS
D
SAS
30

Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN

Question illustration
A
AAS
B
SSS
C
ASA
D
SAS
31

Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

Question illustration
A
LO ≅ LM
B
OA ≅ MA
C
LOA ≅ LMA
Option C
D
LAO ≅ LAM
Option D
32

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

Question illustration
A
a reflection across the line containing AB
B
a rotation about point B
C
a reflection across the line containing CB
D
a rotation about point C
33

Quadrilateral ABCD is translated down and left to form quadrilateral OLMN.

Question illustration
A
5 units
B
6 units
C
8 units
D
10 units
34

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

A
ΔXYZ ≅ ΔTUV
B
ΔXYZ ≅ ΔVUT
C
No congruency statement can be made because only two angles in each triangle are known.
D
No congruency statement can be made because the side lengths are unknown.
35

Quadrilateral L M N O is reflected over a line to form quadrilateral C D A B.

Question illustration
A
AB
B
AD
C
CB
D
DC
36

Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM.If MV measures 3 cm, which other segment must measure 3 cm?

A
AF
B
KJ
C
FD
D
GJ
37

Which congruence theorem can be used to prove △WXS ≅ △YZS?

Question illustration
A
SSS
B
ASA
C
SAS
D
HL
38

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

A
Triangles Q R A and K P A are connected at point A. Triangle K P A is rotated to form triangle Q R A.
Option A
B
Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.
Option B
C
Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.
Option C
D
Triangles Q R A and K P L are shown. Triangle Q R A is rotated about point A and then is shifted down and to the left to form triangle K P L.
Option D
39

The triangles shown are congruent by the SSS congruence theorem.

Question illustration
A
rotation, then reflection, then translation
B
rotation, then translation, then reflection
C
translation, then reflection, then rotation
D
translation, then rotation, then reflection
40

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 4, 4), (negative 4, 1), and (0, 1). Triangle W R S has points (0, negative 1), (1.75, 1.5), (5, negative 1).

Question illustration
A
10 units
B
11 units
C
12 units
D
13 units

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