AnswersAZ-Geometry A MA201Triangle Congruence: ASA and AAS

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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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
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

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
5

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
6

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
7

Given: and are right angles; ; Prove:

Question illustration
A
ASA congruence theorem.
B
AAS congruence theorem.
C
third angle theorem.
D
reflexive property.
8

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
9

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.
10

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

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