Chapter 6, Problem 13RP

Solution

To Prove: The congruency of $\angle PAR$ with respect to $\angle PBR$

Given information: $\overleftrightarrow{PR}\perp m$ and $\angle PAB\cong \angle PBA$ is provided in the question which will help to find the solution.

Proof: Here, PA = PB (sides opposite to equal angles are equal)

And, $\angle PQA=\angle AQR$ (right angle)

So, PA = AR (sides opposite to equal angles are equal)

And, $\angle PBA=\angle ABR=\angle PAB$

Here, AR = PB

And, $\angle PBR=\angle PBQ+\angle QBR$

  $\angle PAR=\angle PAB+\angle BAR$

Hence, $\angle PAR\cong \angle PBR$