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Triangle Congruence: ASA and AAS Answers

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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
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 of these triangle pairs can be mapped to each other using a reflection and a translation?

A
Triangles L R K and A R Q are connected at point R. Triangle L R K is reflected across point R to form triangle A R Q.
Option A
B
Triangles L P K and Q R A are shown. Triangle L P K is reflected across a line to form triangle Q R A. Triangle Q R A is shifted to the right of triangle L P K.
Option B
C
Triangles L P K and Q R A are shown. Triangle L P K is shifted down and to the left to form triangle Q R A.
Option C
D
Triangles L P K and Q R A are shown. Triangle L P K is rotated to form triangle Q R A. Triangle Q R A is also shifted to the right.
Option D
4

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
5

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.
6

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
7

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.
8

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.
9

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
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.

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