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The problem is a geometric proof involving triangle congruence. You are given:

- \( \angle D \cong \angle C \)
- \( \angle CAB \cong \angle DBA \)

You need to prove that triangles \( \triangle ABC \cong \triangle BAD \).

### Analysis:
From the given information, we already know two pairs of congruent angles:
1. \( \angle D \cong \angle C \) (Given)
2. \( \angle CAB \cong \angle DBA \) (Given)

### Steps to complete the proof:

#### Step 3: 
The segments \( AB \) and \( BA \) are congruent by the **Reflexive Property**, which is stated in Step 2.

#### Step 4: 
At this point, you have two angles and the included side congruent between the two triangles (i.e., Angle-Side-Angle, ASA). Therefore, by the **ASA Postulate**, we can conclude that:
- \( \triangle ABC \cong \triangle BAD \)

This proves the required statement.

Would you like to explore any more details or ask specific questions?

### Related Questions:
1. What is the ASA Postulate, and how does it help in triangle congruence?
2. Why is the Reflexive Property useful in geometric proofs?
3. Can the SSA condition (two sides and a non-included angle) ever prove triangle congruence?
4. What other congruence postulates exist besides ASA?
5. How does knowing angle congruence help in determining side congruence?

### Tip:
In any geometric proof involving triangle congruence, always look for congruent angles and sides that correspond directly between the triangles for a valid proof technique like ASA, SSS, or SAS.

Given ∠D ≅ ∠C and ∠CAB ≅ ∠DBA, prove: ∆ABC ≅ ∆BAD.

Learn how to prove triangle congruence for ∆ABC ≅ ∆BAD using the ASA Postulate and Reflexive Property. This geometric proof involves given congruent angles and uses the Angle-Side-Angle method. Suitable for students in Grades 8-10.

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