AnswersGeometryTriangle Congruence: ASA and AAS

Triangle Congruence: ASA and AAS — Quiz Answers

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1
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Which of these triangle pairs can be mapped to each other using two reflections?

A
Image with description Triangles X Y Z and Z A T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle Z A T. Side X Z is congruent to Z T. Angles Z A T, and X Y Z are right angles. Angle X Z Y is congruent to Z T A.
B
Image with description 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. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.
C
Image with description 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. Side X Z is congruent to side P T, angle X Y Z is congruent to angle T Y P, and angle X Z Y is congruent to angle Y T P.
D
Image with description 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. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.
2
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Which shows two triangles that are congruent by AAS?

A
Image with description 2 triangles are connected at one side. The triangles have 2 congruent sides and a congruent angle. The first triangle is rotated and then translated down to form the second triangle.
B
Image with description 2 triangles are connected at one side. The side lengths of the first triangle are congruent to the side lengths of the second triangle.
C
Image with description 2 right triangles are connected at one side. The triangles have a congruent side and a congruent angle. The second triangle is a reflection of the first triangle.
D
Image with description 2 right triangles are connected at one side. The triangles have a congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle.
3

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

A
Image with description 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. Side K P is congruent to Q R, angle L P K is congruent to angle Q R A, and angle L K P is congruent to Q A R.
B
Image with description 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. Side K P is congruent to side Q R, angle Q A R is congruent to angle K L A, and angle K P L is congruent to angle Q R A.
C
Image with description 2 Triangles L P K and Q R A are shown in which the side K P is congruent to side Q R, angle K P L is congruent to angle Q R A, and angle K L P is congruent to angle Q A R.
D
Image with description 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. RK is congruent to QR, Angle K L R is congruent to R A Q.
4

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

A
Image with description 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.. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
B
Image with description 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. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
C
Image with description 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. Angle Q A R is congruent to angle K A P, side R A is congruent to A P, and angle Q R A is congruent to angle K P A.
D
Image with description 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.. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
5

Which shows two triangles that are congruent by ASA?

A
Image with description 2 right triangles are connected at one side. The triangles have 2 congruent sides and one congruent angle.
B
Image with description 2 triangles have 3 congruent angles. The second triangle is to the right of the first triangle.
C
Image with description 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.
D
Image with description 2 triangles have 2 congruent sides and a congruent angle. The first triangle is reflected across a line and then rotated to form the second triangle.
6

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

A
Image with description Triangles X Y Z and Z A T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle Z A T. Side X Z is congruent to Z T. Angles Z A T, and X Y Z are right angles. Angle X Z Y is congruent to Z T A.
B
Image with description 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. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.
C
Image with description 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. Side X Z is congruent to side P T, angle X Y Z is congruent to angle T Y P, and angle X Z Y is congruent to angle Y T P.
D
Image with description 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. Side X Y is congruent to side Y T, angle X Y Z is a right angle, equal to angle Y A T, and angle X Z Y is equal to angle Y T A.
7

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

A
angle cap b is congruent to angle cap p and line segment cap b cap c is congruent to line segment cap p cap q
B
angle cap A is congruent to angle cap t and cap A cap c is equal to cap t cap q is equal to 3 point 2 cm
C
angle cap A is congruent to angle cap t and line segment cap b cap c is congruent to line segment cap p cap q
D
angle cap A is congruent to angle cap t and angle cap b is congruent to angle cap p
E
cap A cap c is equal to cap t cap q is equal to 3 point 2 cm and cap c cap b is equal to cap q cap p is equal to 2 point 2 cm
8

What additional information could be used to prove that the triangles are congruent using AAS? Choose two correct answers.

A
m angle cap c is equal to 35 degrees and m angle cap q is equal to 35 degrees
B
mathrm cap A cap c is equal to 3 point 9 centimeters and cap r cap q is equal to 3 point 9 centimeters
C
cap A cap b is equal to 2 point 5 centimeters and cap m cap q is equal to 2 point 5 centimeters
D
line segment cap c cap b is congruent to line segment cap q cap m
E
angle cap c is congruent to angle cap q
9

Are the triangles congruent? Why or why not?

A
Yes, all the angles of each of the triangles are acute.
B
Yes, they are congruent by either ASA or AAS.
C
No, the congruent sides do not correspond.
D
No, angle cap b is not congruent to angle cap q .
10

What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?

A
line segment cap n cap l is congruent to line segment cap m cap p
B
angle cap l is congruent to angle cap p
C
angle cap n is congruent to angle cap m
D
line segment cap n cap k is congruent to line segment cap m cap q
11

Are the triangles congruent? Why or why not?

A
Yes, all the angles of each of the triangles are acute.
B
No, angle cap b is not congruent to angle cap q .
C
Yes, they are congruent by either ASA or AAS.
D
No, the congruent sides do not correspond.
12

What additional information could be used to prove that the triangles are congruent using AAS? Choose two correct answers.

A
mathrm cap A cap c is equal to 3 point 9 centimeters and cap r cap q is equal to 3 point 9 centimeters
B
m angle cap c is equal to 35 degrees and m angle cap q is equal to 35 degrees
C
line segment cap c cap b is congruent to line segment cap q cap m
D
cap A cap b is equal to 2 point 5 centimeters and cap m cap q is equal to 2 point 5 centimeters
E
angle cap c is congruent to angle cap q
13

Which shows two triangles that are congruent by ASA?

A
Image with description 2 right triangles are connected at one side. The triangles have 2 congruent sides and one congruent angle.
B
Image with description 2 triangles have 2 congruent sides and a congruent angle. The first triangle is reflected across a line and then rotated to form the second triangle.
C
Image with description 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.
D
Image with description 2 triangles have 3 congruent angles. The second triangle is to the right of the first triangle.
14

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

A
Image with description 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.. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
B
Image with description 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. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
C
Image with description 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.. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.
D
Image with description 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. Angle Q A R is congruent to angle K A P, side R A is congruent to A P, and angle Q R A is congruent to angle K P A.
15

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

A
Image with description 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. Side K P is congruent to side Q R, angle Q A R is congruent to angle K L A, and angle K P L is congruent to angle Q R A.
B
Image with description 2 Triangles L P K and Q R A are shown in which the side K P is congruent to side Q R, angle K P L is congruent to angle Q R A, and angle K L P is congruent to angle Q A R.
C
Image with description 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. RK is congruent to QR, Angle K L R is congruent to R A Q.
D
Image with description 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. Side K P is congruent to Q R, angle L P K is congruent to angle Q R A, and angle L K P is congruent to Q A R.
16

Which shows two triangles that are congruent by AAS?

A
Image with description 2 right triangles are connected at one side. The triangles have a congruent side and 2 congruent angles. The second triangle is a reflection of the first triangle.
B
Image with description 2 triangles are connected at one side. The triangles have 2 congruent sides and a congruent angle. The first triangle is rotated and then translated down to form the second triangle.
C
Image with description 2 right triangles are connected at one side. The triangles have a congruent side and a congruent angle. The second triangle is a reflection of the first triangle.
D
Image with description 2 triangles are connected at one side. The side lengths of the first triangle are congruent to the side lengths of the second triangle.
17

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

A
angle cap b is congruent to angle cap p and line segment cap b cap c is congruent to line segment cap p cap q
B
cap A cap c is equal to cap t cap q is equal to 3 point 2 cm and cap c cap b is equal to cap q cap p is equal to 2 point 2 cm
C
angle cap A is congruent to angle cap t and line segment cap b cap c is congruent to line segment cap p cap q
D
angle cap A is congruent to angle cap t and angle cap b is congruent to angle cap p
E
angle cap A is congruent to angle cap t and cap A cap c is equal to cap t cap q is equal to 3 point 2 cm
18

What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?

A
line segment cap n cap k is congruent to line segment cap m cap q
B
angle cap n is congruent to angle cap m
C
angle cap l is congruent to angle cap p
D
line segment cap n cap l is congruent to line segment cap m cap p
19

Which statements are true about additional information for proving that the triangles are congruent? Choose two correct answers.

A
If angle cap c and angle cap q are right angles, then triangles would be congruent.
B
If all the angles are acute, then the triangles would be congruent.
C
If line segment cap b cap c is congruent to line segment cap p cap q , then the triangles would be congruent by ASA.
D
If angle cap b is congruent to angle cap p , then the triangles would be congruent by AAS.
E
If angle cap A is congruent to angle cap t , then the triangles would be congruent by ASA.

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