Answer
1) Prove $\overline{CE}\cong\overline{CB}$
2) Prove $\angle ACB\cong\angle DCE$
3) Prove $\angle B\cong\angle E$
4) Use method ASA to prove triangles congruent.
Work Step by Step
1) It is given that $C$ is the midpoint of $\overline{EB}$.
So, $\overline{CE}\cong\overline{CB}$.
2) It is also given that $\overline{AD}\bot\overline{BE}$
So, $\angle ACB=90^{\circ}$ and $\angle DCE=90^{\circ}$
That means $\angle ACB\cong\angle DCE$
3) We have $\overline{AB}\parallel\overline{ED}$ and $\overline{BE}$ cuts through both $\overline{AB}$ and $\overline{ED}$.
Therefore, $\angle B\cong\angle E$ (2 alternate interior angles).
4) From the results in 1), 2) and 3), according to method ASA, $\triangle ABC\cong\triangle DEC$.
