Question

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle RST is congruent to triangle RSQ given that RS ⊥ ST, RS ⊥ SQ, and ∠STR ≅ ∠SQR. Submit the entire proof to your instructor.
Given:
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR

Prove:
△RST ≅ △RSQ        

Statement
1. RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR
2.
3.
4.△RST ≅ △RSQ
Reason
1.
2.
3.
4.

Answer 1

Answer:

             Statements                                          Reasons

1.  RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR             Given

2. ∠RST ≅ ∠RSQ                                             Definition of right angles

3.   RS ≅ RS                                                      Reflexive property

4.  △RST ≅ △RSQ                                            AAS postulate

Step-by-step explanation:

Given: RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR.

To prove: △RST ≅ △RSQ

Proof:

In triangle RST and RSQ,

∠STR ≅ ∠SQR             (Given)

∠RST ≅ ∠RSQ             (Definition of right angles)

RS ≅ RS                       (Reflexive property)

In triangle RST and RSQ, two angles and the non-included side of △RST are congruent to two angles and the non-included side of △RSQ. So, by AAS postulate both triangles are congruent.

△RST ≅ △RSQ             (AAS postulate)

Hence proved.

Answer 2

1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property