Answer
With the information given, it follows that $\triangle ABC\cong\triangle EDC$, according to method AAS.
Work Step by Step
We are given that
- $\angle A\cong\angle E$
- $\overline{BC}\cong\overline{DC}$
We see that $\overline{AD}$ intersects $\overline{BE}$ at $C$.
So, $\angle ACB\cong\angle ECD$
We now have 2 angles and a non-included side of $\triangle ABC$ are congruent with 2 corresponding angles and a non-included side of $\triangle EDC$.
Therefore, according to method AAS, $\triangle ABC\cong\triangle EDC$.
