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The task is to complete a proof to show that triangles \( \triangle AED \cong \triangle BED \). Based on the given information, I will help you fill out the table of justifications.

### Steps:
1. **Given Information**: 
   - \( \angle AED \cong \angle BED \)
   - \( \angle EAD \cong \angle CBF \)

2. **Statement 2**: 
   \( \angle CBF \cong \angle DBE \)

   **Justification**: **Given** — It states that these angles are congruent.

3. **Statement 3**: 
   \( \angle EAD \cong \angle DBE \)

   **Justification**: **Transitive Property** — Since \( \angle EAD \cong \angle CBF \) and \( \angle CBF \cong \angle DBE \), by the transitive property, \( \angle EAD \cong \angle DBE \).

4. **Statement 4**: 
   \( DE \cong DE \)

   **Justification**: **Reflexive Property** — Any segment is congruent to itself.

5. **Statement 5**: 
   \( \triangle AED \cong \triangle BED \)

   **Justification**: **Angle-Angle-Side (AAS)** — Two angles and the non-included side are congruent, so the triangles are congruent.

### Complete Table:
| **Statement**                                   | **Justification**        |
|-------------------------------------------------|--------------------------|
| \( \angle AED \cong \angle BED \) and \( \angle EAD \cong \angle CBF \) | Given                    |
| \( \angle CBF \cong \angle DBE \)               | Given                    |
| \( \angle EAD \cong \angle DBE \)               | Transitive Property       |
| \( DE \cong DE \)                               | Reflexive Property        |
| \( \triangle AED \cong \triangle BED \)         | Angle-Angle-Side (AAS)    |

Would you like a detailed explanation of each step or have any further questions?

### Additional Related Questions:
1. How does the Angle-Angle-Side (AAS) congruence rule work?
2. What is the difference between the transitive and reflexive properties?
3. How do you identify congruent triangles using other congruence criteria (like SSS, SAS)?
4. What are vertical angles and how are they used in triangle congruence?
5. How does knowing two pairs of angles and a side help in proving triangle congruence?

### Tip:
When proving triangle congruence, always identify whether the given angles or sides are included (shared) between the triangles to decide on the correct congruence rule.

Prove that triangle AED is congruent to triangle BED based on the given angles and segments.

This problem demonstrates how to prove that triangle AED is congruent to triangle BED using the Angle-Angle-Side (AAS) congruence rule. The proof involves the use of the transitive property and reflexive property in geometry. Suitable for students in Grades 8-10.

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