AnswersQ5 Geometry New 2022Congruent Figures

Congruence in Right Triangles Answers

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1
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Analyze the diagram below and answer the question that follows. is a rectangle. Why is ? Explain your reasoning.

Question illustration
A
1) , reflexive property of congruence 2) , opposite sides of a rectangle are congruent 3) by the AAS theorem
B
1) , reflexive property of congruence 2) , opposite sides of a rectangle are congruent 3) and are right triangles, because all angles in a rectangle are right angles 4) by the HL theorem
C
1) , reflexive property of congruence 2) , opposite sides of a rectangle are congruent
D
not enough information
2
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If the __________ and a leg of one triangle are congruent to the hypotenuse and a __________ of another triangle, then the triangles are congruent by the HL theorem.

A
hypotenuse . . . leg
B
leg . . . leg
C
leg . . . hypotenuse
D
right angle . . . leg
3

Which pair of triangles can be proven congruent by using the HL theorem? A. B. C. D. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
4

Analyze the diagram below and complete the instructions that follow.Photo by Matt ReinboldIn the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.

Question illustration
A
84 feet
B
94 feet
C
168 feet
D
186 feet
5

Analyze the diagram below and complete the instructions that follow. Using HL, determine whether . Explain your reasoning.

Question illustration
A
Yes, the triangles are congruent by HL. 1) , given 2) , given
B
Yes, the triangles are congruent by HL. 1) and are right triangles 2) , given 3) , given
C
No, not enough information is given to justify congruence.
D
No, the triangles do not have corresponding congruent legs.
6

Given: is perpendicular to , which is the base of isosceles Prove: Statements Reasons 1) is isosceles, 1) given 2) 2) 3) and are right angles 3) 4) 4) definition of right triangle 5) 5) 6) 6)

Question illustration
A
2) definition of an isosceles triangle 3) definition of perpendicular 5) symmetric property of congruence 6) HL theorem
B
2) reflexive property of congruence 3) definition of perpendicular 5) definition of an isosceles triangle 6) SAS theorem
C
2) definition of an isosceles triangle 3) definition of perpendicular 5) reflexive property of congruence 6) HL theorem
D
There is not enough information to prove the triangles congruent.
7

Analyze the diagram below and complete the instructions that follow. is an isosceles triangle with base . Determine whether by the HL theorem. Explain your reasoning. The diagram is not to scale.

Question illustration
A
1) , given 2) , definition of an isosceles triangle 3) by the HL theorem
B
1) , given 2) , definition of an isosceles triangle 3) , all right angles are congruent 4) by the HL theorem
C
1) , given 2) , definition of an isosceles triangle
D
The triangles are not right triangles, so the HL theorem cannot be used to prove congruence.
8

Given the diagram below and the fact that , prove . Statements Reasons 1) , and are right angles 1) 2) 2) 3) and are right triangles 3) 4) 4)

Question illustration
A
1) Given 2) All right angles are congruent 3) Reflexive property of congruence 4) HL theorem
B
1) Given 2) Reflexive property of congruence 3) Definition of right triangle 4) HL theorem
C
1) Given 2) Reflexive property of congruence 3) Definition of right triangle 4) SAS theorem
D
There is not enough information to prove the triangles congruent.
9

Analyze the diagram below and answer the question that follows. Which of the following statements would not provide enough information to prove using the HL theorem? A. B. C. D. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
10

Analyze the diagram below and answer the question that follows. Which two triangles are congruent by the HL theorem?

Question illustration
A
a and b
B
b and c
C
a and c
D
None of the triangles are congruent by the HL theorem.

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