Elementary Geometry for College Students (5th Edition)

With the information given, it does not follow that $\triangle ABC\cong\triangle EDC$.
We are given that - $\angle A\cong\angle E$ - $\angle B\cong\angle D$ We see that $\overline{AD}$ intersects $\overline{BE}$ at $C$. So, $\angle ACB\cong\angle ECD$ Eventually, we are given 2 congruent pairs of angles and can deduce one more congruent pair of angles from the given information. However, 3 congruent pairs of angles are not enough to conclude that 2 triangles are congruent. We need at least one more congruent pair of sides, but the information given is not enough to do so. Therefore, with the information given, it does not follow that $\triangle ABC\cong\triangle EDC$.