Question

1. which reason justifies the conclusion that (overline{pv}congoverline{pr}) when (\triangle ptvcong\triangle ptr)?

list of multiple - choice options (partially visible in ocr: cpctc, sas theorem, asa theorem, sss theorem)

Explanation:

Step1: Recall triangle - congruence postulates

In triangle - congruence, SSS (Side - Side - Side) means if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. SAS (Side - Angle - Side) means if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. ASA (Angle - Side - Angle) means if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. AAS (Angle - Angle - Side) means if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Step2: Analyze the given situation

We want to prove $\triangle PVS\cong\triangle PVR$. If we know that $\angle VPS=\angle VPR$ (an angle), $PV = PV$ (common side), and $PS = PR$ (a side), we have two sides and the included angle of $\triangle PVS$ and $\triangle PVR$ being congruent.

Answer:

SAS Postulate