Chapter 6, Problem 11RP

Solution

To Prove: The congruency of $\angle ABQ$ with respect to $\angle BAQ$

Given information: $\overline{BP}\perp \overline{PQ}$ , $\overline{AP}\perp \overline{PQ}$ and A and B are equidistant from P is provided in the question which will help to find the solution.

Proof: PA = PB (given)

Hence, $\angle ABP=\angle BAP$ (angle opposite to equal sides are equal)

A and B are equidistant from P, then if we take AQ and BQ then they are also equal.

And, $\angle BPQ=\angle APQ$ (right angle)

So that, BQ = AQ (sides opposite to equal angles are equal)

So that, $\angle BAQ\cong \angle ABQ$