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The problem asks to prove that triangles \( \triangle ABC \cong \triangle EDC \) using the given information. Let's break down the proof using the given statements:

1. **Given: \( BC \cong DC \) and \( AC \cong EC \)** 
   - This is already marked in the table. These are sides of the triangles, so this is the **Given** information.

2. **Step 3: \( \angle ACB \cong \angle ECD \)** 
   - These are **vertical angles**, which are always congruent when two lines intersect. This provides the third pair of congruent components.

3. **Step 4: \( \triangle ABC \cong \triangle EDC \)** 
   - Now that we have two sides and the included angle congruent, we can use the **SAS (Side-Angle-Side) Congruence Postulate** to conclude that the two triangles are congruent.

So, filling in the reasons for the proof:

- Statement 1: \( BC \cong DC \) → **Given**
- Statement 2: \( AC \cong EC \) → **Given**
- Statement 3: \( \angle ACB \cong \angle ECD \) → **Vertical Angles Theorem**
- Statement 4: \( \triangle ABC \cong \triangle EDC \) → **SAS Congruence Postulate**

Does this explanation help? Would you like any further details?

Here are some related questions to deepen your understanding:
1. How do you determine when to use the SAS Congruence Postulate?
2. What other congruence postulates could apply if more information were provided?
3. Can you explain why vertical angles are always congruent?
4. How would the proof change if the angle was not included between the two congruent sides?
5. What are other ways to prove triangle congruence without knowing any angles?

**Tip:** Always ensure you check if the congruent sides and angles correspond to the same parts of the triangles when using congruence postulates.

Use the given information to prove that \( \triangle ABC \cong \triangle EDC \). Given: BC \cong DC, AC \cong EC.

Learn how to prove that triangles ABC and EDC are congruent using the SAS Congruence Postulate and the Vertical Angles Theorem. This problem is designed for students in Grades 9-11 and covers key concepts in triangle congruence.

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