Chapter 4.4, Problem 13PPS

To determine

To prove:

  $\Delta PRQ\cong \Delta TRS$ .

Explanation of Solution

Given Information:

  $R$ is the midpoint of $\overline{QS}$ and $\overline{PT}$ .

  

Proof:

Since $R$ is the midpoint of $\overline{QS}$ and $\overline{PT}$ , $\overline{PR}\cong \overline{RT}$ and $\overline{RS}\cong \overline{RS}$ by definition of a midpoint. $\angle PRQ\cong \angle TRS$ by theVertical Angles Theorem.

So, $\Delta PRQ\cong \Delta TRS$ by SAS.