Exercise 3 Page 651

From the given information, we know that ∠ P ≅ ∠ T. Also, since the triangles share R as a vertex, we know this angle is congruent by the Reflexive Property of Congruence. Let's separate the triangles and add the given information.

Since the triangles have two angles and a non-included side that are congruent, we can claim that △ SRP ≅ △ QRT by the AAS Congruence Theorem.

Proof

Two-Column Proof

Let's also show this as a two-column proof.

Statement	Reason
1. QR ≅ RS, ∠ P ≅ ∠ T	1. Given
2. ∠ QRT ≅ ∠ SRP	2. Reflexive Property of Congruence
3. △ SRP ≅ △ QRT	3. AAS Congruence Theorem