Elementary Geometry for College Students (5th Edition)

With the information given, it follows that $\triangle ABC\cong\triangle EDC$, according to method AAS.
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, $\triangle ABC\cong\triangle EDC$.