Given that PQ ≅ SR and ∠POR ≅ ∠SRO, and knowing that PR ≅ PR (Reflexive Property), we can conclude that △POR ≅ △SRO (ASA Postulate).
The problem at hand involves proving the congruence of two triangles, POR and SRO, given that line segment PQ is congruent to SR and angle POR is congruent to angle SRO. This can be achieved using the Angle-Side-Angle (ASA) postulate for triangle congruence. The ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Here's the proof:
Statements:
1. PQ ≅ SR
2. ∠POR ≅ ∠SRO
3. PR ≅ PR
4. △POR ≅ △SRO
Reasons:
1. Given
2. Given
3. Reflexive Property of Congruence
4. ASA Postulate
The first two statements are given in the problem: line segment PQ is congruent to SR, and angle POR is congruent to angle SRO. The third statement is derived from the Reflexive Property of Congruence, which states that any geometric figure is congruent to itself. In this case, line segment PR is a side of both triangles, so it is congruent to itself. With these three congruences, we can apply the ASA postulate to conclude that triangle POR is congruent to triangle SRO.