To complete the proof, let’s proceed step-by-step to prove that $AE \cong BE$ based on the given conditions.

Given:

1. $AD \cong BC$
2. $\angle D \cong \angle C$

To Prove: $AE \cong BE$

Proof Steps:

1. Statement: $AD \cong BC$

   • Reason: Given

2. Statement: $\angle D \cong \angle C$

   • Reason: Given

3. Statement: $\triangle ADE \cong \triangle BCE$

   • Reason: SAS (Side-Angle-Side) Congruence Postulate
     • Explanation: In $\triangle ADE$ and $\triangle BCE$:
       • Side $AD \cong BC$ (given).
       • Angle $\angle D \cong \angle C$ (given).
       • Side $DE = CE$ (common side in both triangles).

4. Statement: $AE \cong BE$

   • Reason: Corresponding Parts of Congruent Triangles (CPCTC)