AnswersAZ-Geometry A MA201Triangles and Their Side Lengths

Triangle Congruence: SSS and HL Answers

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1
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Triangles L K N and P Q M are shown. Sides K L and Q P are congruent. Angles L K N and P Q M are right angles.

Question illustration
A
NL ≅ MP
B
NK ≅ MQ
C
N ≅ M
Option C
D
L ≅ P
Option D
2
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Which of these triangle pairs can be mapped to each other using two reflections?

A
Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T.
Option A
B
Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T.
Option B
C
Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T.
Option C
D
Triangles X Y Z and A Z T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle A Z T.
Option D
3

Which shows two triangles that are congruent by AAS?

Question illustration
A
2 right triangles are connected at one side. The triangles have 1 congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle.
Option A
B
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated to form the second triangle.
Option B
C
2 triangles are connected at one side. All sides are congruent.
Option C
D
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.
Option D
4

Which shows two triangles that are congruent by ASA?

Question illustration
A
2 right triangles are connected at one side. The triangles have 2 congruent sides and one congruent angle.
Option A
B
2 triangles are connected at one side. The triangles also have 2 congruent angles. The first triangle can be rotated to form the second triangle.
Option B
C
2 triangles have 3 congruent angles. The second triangle is to the right of the first triangle.
Option C
D
2 triangles have 2 congruent sides and 1 congruent angles. The first triangle is reflected across a line and then rotated to form the second triangle.
Option D
5

What additional information could be used to prove that the triangles are congruent using AAS? Select two options.

A
C ≅ Q
Option A
B
CB ≅ QM
C
AC = 3.9cm and RQ = 3.9cm
D
mC = 35° and mQ = 35°
Option D
E
AB = 2.5cm and MQ = 2.5cm
6

Given: and are right angles; Prove:

Question illustration
A
of the ASA congruence theorem.
B
of the AAS congruence theorem.
C
of the third angle theorem.
D
all right triangles are congruent.
7

The proof ABC ≅ DCB that is shown.Given: A ≅ D; CD||ABProve: ABC ≅ DCB

Question illustration
A
alt. ext. s are ≅
Option A
B
ASA
C
AAS
D
corr. int. s are ≅
Option D
8

What additional information could be used to prove that the triangles are congruent using AAS or ASA? Select three options.

A
B ≅ P and BC ≅ PQ
Option A
B
A ≅ T and AC = TQ = 3.2cm
Option B
C
A ≅ T and B ≅ P
Option C
D
A ≅ T and BC ≅ PQ
Option D
E
AC = TQ = 3.2 cm and CB = QP = 2.2 cm
9

Which statements are true about additional information for proving that the triangles are congruent? Select two options.

A
If A ≅ T, then the triangles would be congruent by ASA.
Option A
B
If B ≅ P, then the triangles would be congruent by AAS.
Option B
C
If all the angles are acute, then the triangles would be congruent.
D
If C and Q are right angles, then triangles would be congruent.
Option D
E
If BC ≅ PQ, then the triangles would be congruent by ASA.
10

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.
11

Which statements are true about additional information for proving that the triangles are congruent? Select two options.

A
If A ≅ T, then the triangles would be congruent by ASA.
Option A
B
If B ≅ P, then the triangles would be congruent by AAS.
Option B
C
If all the angles are acute, then the triangles would be congruent.
D
If C and Q are right angles, then triangles would be congruent.
Option D
E
If BC ≅ PQ, then the triangles would be congruent by ASA.
12

Which of these triangle pairs can be mapped to each other using two reflections?

A
Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T.
Option A
B
Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T.
Option B
C
Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T.
Option C
D
Triangles X Y Z and A Z T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle A Z T.
Option D
13

The proof ABC ≅ DCB that is shown.Given: A ≅ D; CD||ABProve: ABC ≅ DCB

Question illustration
A
alt. ext. s are ≅
Option A
B
ASA
C
AAS
D
corr. int. s are ≅
Option D
14

Triangles J K L and M N Q are shown. Triangle J K L is rotated slightly about point L to form triangle M N Q.

Question illustration
A
a reflection across the line containing LK
B
a reflection across the line containing JK
C
a rotation about point L
D
a rotation about point K
15

Which shows two triangles that are congruent by AAS?

A
2 right triangles are connected at one side. The triangles have 1 congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle.
Option A
B
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated to form the second triangle.
Option B
C
2 triangles are connected at one side. All sides are congruent.
Option C
D
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.
Option D
16

What additional information could be used to prove that the triangles are congruent using AAS? Select two options.

A
C ≅ Q
Option A
B
CB ≅ QM
C
AC = 3.9cm and RQ = 3.9cm
D
mC = 35° and mQ = 35°
Option D
E
AB = 2.5cm and MQ = 2.5cm
17

Triangles M Z K and Q Z K share side Z K. Angles M K Z and Z K Q are congruent. Angles K Z M and K Z Q are both right angles.

Question illustration
A
a rotation about point K
B
a reflection across the line containing MZ
C
a reflection across the line containing ZK
D
a rotation about point Z
18

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
19

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.
20

Triangles L K N and P Q M are shown. Sides K L and Q P are congruent. Angles L K N and P Q M are right angles.

Question illustration
A
NL ≅ MP
B
NK ≅ MQ
C
N ≅ M
Option C
D
L ≅ P
Option D

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