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.

             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.

step-by-step explanation:

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