The problem is to complete a proof that triangle $POR$ is congruent to triangle $TSR$. We are given that $OE$ is congruent to $TS$, $PE$ is congruent to $PR$, and angle $PRO$ is congruent to angle $TRS$. The task is to find the reason why $\triangle POR \cong \triangle TSR$.

1. Problem Description

The problem is to complete a proof that triangle $POR$ is congruent to triangle $TSR$. We are given that $OE$ is congruent to $TS$, $PE$ is congruent to $PR$, and angle $PRO$ is congruent to angle $TRS$. The task is to find the reason why $\triangle POR \cong \triangle TSR$.

2. Solution Steps

We are given:

1. $OE \cong TS$ (Given)

2. $PE \cong PR$ (Given)

3. $\angle PRO \cong \angle TRS$ (Given)

From the given information, we have two sides and an included angle.

Therefore, we can use the SAS (Side-Angle-Side) Congruence Postulate to prove the triangles are congruent.

SAS Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In our case, we have $PR \cong TS$, $\angle PRO \cong \angle TRS$, and $OE \cong TS$. The first two correspond to the sides and angle. However, it appears that $OE$ should be $OR$. However, we don't know what $OE$ or $OR$ is. Because of typo of given information $OR \cong TR$, it must be $OR$ congruent to $TR$ instead of $OE$ congruent to $TS$. Therefore, $\triangle POR \cong \triangle TSR$ by SAS.

3. Final Answer

SAS Congruence Postulate