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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)**

Given: AD ≅ BC and ∠D ≅ ∠C. Prove: AE ≅ BE.

Learn how to prove AE ≅ BE given that AD ≅ BC and ∠D ≅ ∠C, using the SAS Congruence Postulate and CPCTC. This step-by-step solution demonstrates triangle congruence and is ideal for high school geometry students.

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