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:

Give the statement: $RS \perp ST$ , $RS \perp SQ$ and

$\angle STR \cong SQR$

Perpendicular means if a line meeting another at a right angle or 90°

In Δ RST and Δ RSQ

$RS \perp ST$              [Given]

$RS \perp SQ$

By definition of perpendicular;

$\angle RST \cong \angle RSQ =90^{\circ}$   [Angle]

$\angle STR \cong SQR$   [Angle]           [Given]

Reflexive property states that a value is equal to itself.

$RS \cong RS$  [Side]        [Reflexive property ]

AAS(Angle -Angle -Side] Postulates states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent.

Then, by AAS postulates;

$\triangle RST \cong \triangle RSQ$

Two column proof:

Statement                                         Reason

1. $RS \perp ST$,                                  Given  

$RS \perp SQ$

$\angle STR \cong SQR$

2. $\angle RST \cong \angle RSQ =90^{\circ}$       def. of perpendicular

3. $RS \cong RS$                                 by  Reflexive property

4. △RST ≅ △RSQ                                            AAS postulates.

Answer 2

I see the solution in three steps.
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property