https://file.aiquickdraw.com/mathbot/file/17297949947448ob10fp9.jpg

To complete the proof, the missing step would be to establish the congruence of triangles \( \triangle ABE \) and \( \triangle CDE \).

### Step-by-Step Reasoning:

1. **Step 5: \( \triangle ABE \cong \triangle CDE \)**

   - **Reason**: **ASA (Angle-Side-Angle) Congruence Postulate**.

### Explanation:

- In the table, you already have:
  1. \( AB \parallel DC \) and \( AB \cong DC \) (Given).
  2. \( \angle A \cong \angle C \) (Alternate interior angles due to parallel lines cut by a transversal).
  3. \( \angle B \cong \angle D \) (Same reasoning as above).
  4. \( DC \cong DC \) (Reflexive Property, as a side is congruent to itself).
  
From these statements:
- You have two pairs of congruent angles (\( \angle A \cong \angle C \) and \( \angle B \cong \angle D \)).
- You also have a pair of congruent sides (\( DC \cong DC \)) between these angles.

Therefore, by the **ASA Congruence Postulate**, \( \triangle ABE \cong \triangle CDE \).

Would you like a detailed explanation on any specific part or have any other questions?

### Related Questions:
1. What is the ASA Congruence Postulate, and how does it work?
2. How does the Reflexive Property help in congruence proofs?
3. What are alternate interior angles, and why are they congruent in this case?
4. What other congruence criteria (e.g., SSS, SAS) could be used in similar proofs?
5. How does the congruence of \( \triangle ABE \) and \( \triangle CDE \) affect other angles in the figure?

**Tip**: In geometry, always look for congruent angles and sides as clues for establishing triangle congruence. They often form the basis of many geometric proofs.

Given AB || DC and AB ≅ DC, prove that ∆ABE ≅ ∆CDE.

This geometry problem demonstrates how to prove ∆ABE ≅ ∆CDE using the ASA Congruence Postulate. The problem involves parallel lines, alternate interior angles, and the reflexive property. Suitable for students in Grades 9-11.

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