Question 1191473: 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 REASON
1.RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR 1.
2. 2.
3. 3.
4. △RST ≅ △RSQ 4.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here is the two-column proof:
**Given:**
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR
**Prove:**
△RST ≅ △RSQ
| STATEMENT | REASON |
|---|---|
| 1. RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | 1. Given |
| 2. ∠RSQ = 90°, ∠RST = 90° | 2. Definition of perpendicular lines |
| 3. ∠RSQ ≅ ∠RST | 3. Transitive Property of Congruence (Both angles are right angles) |
| 4. RS ≅ RS | 4. Reflexive Property of Congruence |
| 5. △RST ≅ △RSQ | 5. Angle-Side-Angle (ASA) Congruence Postulate |
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