AnswersOC27 GEO-1206310-S1-Degele-VOL7006PTriangle Congruence: SAS

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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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.
3

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
4

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
5

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
6

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
7

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
8

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
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

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

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