Chapter 3, Problem 12RP

To determine

To Prove: $\Delta ABE$ is isosceles.

Explanation of Solution

Given information: $\overline{AD}\cong \overline{BC}$ and $\angle DAB\cong \angle CBA$ is provided in the question which will help to find the solution.

Proof: In the given figure, $\overline{AD}\cong \overline{BC}$ (given)

And, $\angle DAB\cong \angle CBA$ (given)

And, we know that diagonals of parallelogram bisect opposite angles of parallelogram

Hence, $\angle EAB=\angle EBA$

So that, EA =EB (sides of equal angles are equal)

Hence, we can say that

  $\Delta ABE$ is isosceles.