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To complete this proof, let’s look at the goal: proving that \( \triangle ABD \cong \triangle BAC \).

Here’s a step-by-step continuation of the proof:

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### Given Information:
1. **\( \triangle AED \cong \triangle BEC \)** and **\( AC \cong BD \)**
2. **Prove:** \( \triangle ABD \cong \triangle BAC \)

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### Proof Steps

1. **\( \triangle AED \cong \triangle BEC \)** and **\( AC \cong BD \)** (Given)
2. **\( AE \cong BE \)** (Corresponding Parts of Congruent Triangles are Congruent, or CPCTC)
3. **\( \angle AED \cong \angle BEC \)** (CPCTC)
4. **\( AB \cong BA \)** (Reflexive Property)
5. **\( \triangle ABD \cong \triangle BAC \)** (SAS Postulate)

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### Explanation of Each Step

- **Step 5 (Final Step)**: We conclude \( \triangle ABD \cong \triangle BAC \) by the **Side-Angle-Side (SAS) Congruence Postulate**:
   - **Side** \( AB \cong BA \) (Reflexive Property),
   - **Angle** \( \angle AED \cong \angle BEC \) (CPCTC),
   - **Side** \( AE \cong BE \) (CPCTC).

Each side and angle pair is congruent, meeting the requirements of the SAS postulate for triangle congruence.

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Would you like further details on any step, or do you have additional questions?

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### Related Questions

1. What is the Side-Angle-Side (SAS) Postulate?
2. Why is CPCTC used in triangle congruence proofs?
3. How does the reflexive property work in congruence proofs?
4. Can the Side-Side-Side (SSS) postulate also prove congruence in this problem?
5. What role do congruent triangles play in geometry proofs?

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### Tip

Always identify corresponding parts of congruent triangles early in the proof, as they often provide key relationships to complete congruence arguments.

Learn how to complete a triangle congruence proof using CPCTC and the SAS postulate. This step-by-step guide is ideal for high school geometry students and covers key concepts in triangle congruence, including the use of CPCTC and the Reflexive Property.

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