Chapter 3.7, Problem 13PSB

To determine

To Prove: Congruency of the $\angle AED$ with respect to $\angle CDE$

Explanation of Solution

Given information: $\overline{BE}\cong \overline{BD}$ , $\overline{BE}\perp \overline{AE}$ , $\angle BDC={90}^{\circ }$ is provided in the question which will help to find the solution.

Proof: Here, $\angle AEB=\angle BDC={90}^{\circ }$

And, BE = BD (given)

And, $\angle BED=\angle BDE$ (angle opposite to equal sides are equal)

And, $\angle AEB+\angle BED=\angle BDC+\angle BED$ ( $\angle BED=\angle BDE$ )

  $\angle AED=\angle CDE$

  $\therefore$

  $\angle AED\cong \angle CDE$