Chapter 4.5, Problem 3PS

To determine

To show: $\overline{AC}\cancel{\cong }\overline{AD}$.

Explanation of Solution

Given information:

A triangle is given as below.

  

  $\angle D\cong \angle ABE,\overline{BE}\cancel{\parallel }\overline{CD}.$

Calculation:

A triangle is given as below.

  

  $\begin{array}{l}\text{In above figure,}\\ \angle D\cong \angle ABE,\overline{BE}\cancel{\parallel }\overline{CD}\\ \Rightarrow \angle D\cancel{\cong }\angle C\\ \Rightarrow \overline{AC}\cancel{\cong }\overline{AD}\left\{\text{Not an isosceles triangle}\right\}\end{array}$