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Lesson 4: Triangle Congruence: ASA and AAS Answers

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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
2
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Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

Question illustration
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
3

Triangles Q R S and T U V are shown. Triangle Q R S is translated across S Q and then is shifted down and to the right to form triangle T U V.

Question illustration
A
No, the triangles are not congruent.
B
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.
C
No, the triangles are obtuse.
D
Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map △QRS to △TUV.
4

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
5

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
6

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
7

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
8

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
9

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
10

Given: and are right angles; ; Prove:

Question illustration
A
ASA congruence theorem.
B
AAS congruence theorem.
C
third angle theorem.
D
reflexive property.

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