Chapter 12.7, Problem 10E

To determine

To prove: The statement $\angle 1\cong \angle 2$ .

Answer to Problem 10E

The proof that $\angle 1\cong \angle 2$ is stated below.

Explanation of Solution

Consider $\Delta ABE$ and $\Delta DEC$ .

  $\begin{array}{c}\angle AEB=\angle DEC\\ \angle A=\angle D\\ \overline{AB}=\overline{DC}\end{array}$

Thus, by AAS congruence theorem.

  $\Delta ABE\cong \Delta DCE$

So,

  $\angle 1\cong \angle 2$

Hence, proved.