Answers Q5 Geometry New 2022Triangle Congruence: ASA Postulate and AAS Theorem

Congruence in Right Triangles Answers

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Analyze the diagram below and complete the instructions that follow. If , find the value of and the length of .

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

a and b

b and c

a and c

None of the triangles are congruent by the HL theorem.

Analyze the diagram below and complete the instructions that follow. The triangles are congruent. Find the length of each hypotenuse.

Analyze the diagram below and complete the instructions that follow. Find the length of each hypotenuse such that . A. B. C. D. Please select the best answer from the choices provided

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)

2) definition of an isosceles triangle 3) definition of perpendicular 5) symmetric property of congruence 6) HL theorem

2) reflexive property of congruence 3) definition of perpendicular 5) definition of an isosceles triangle 6) SAS theorem

2) definition of an isosceles triangle 3) definition of perpendicular 5) reflexive property of congruence 6) HL theorem

There is not enough information to prove the triangles congruent.

Given: quadrilateral GHIJ Prove: Statements Reasons 1) 1) Given 2) 2) Given 3) 3) Definition of right triangle 4) 4) Reflexive property of congruence 5) 5) HL theorem

1) 2) and are right angles 3) and are right triangles 4) 5)

1) and are right angles 2) 3) and are right triangles 4) 5)

1) 2) and are right angles 3) and are isosceles triangles 4) 5)

There is not enough information to prove the triangles congruent.

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)

1) Given 2) All right angles are congruent 3) Reflexive property of congruence 4) HL theorem

1) Given 2) Reflexive property of congruence 3) Definition of right triangle 4) HL theorem

1) Given 2) Reflexive property of congruence 3) Definition of right triangle 4) SAS theorem

There is not enough information to prove the triangles congruent.

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.

1) , given 2) , definition of an isosceles triangle 3) by the HL theorem

1) , given 2) , definition of an isosceles triangle 3) , all right angles are congruent 4) by the HL theorem

1) , given 2) , definition of an isosceles triangle

The triangles are not right triangles, so the HL theorem cannot be used to prove congruence.

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

1) , reflexive property of congruence 2) , opposite sides of a rectangle are congruent 3) by the AAS theorem

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

1) , reflexive property of congruence 2) , opposite sides of a rectangle are congruent

not enough information

Analyze the diagram below and answer the question that follows. Given that is the perpendicular bisector of , which two triangles are congruent by the HL theorem?

and

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Congruence in Right Triangles Answers

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