Geometry

Question Analysis:
This problem involves overlapping triangles △ACB and △ADB.
We must determine which congruence postulates can prove their congruence.

Key Concept Explanation:
ASA (Angle-Side-Angle): Two angles and the included side must be congruent.
AAS (Angle-Angle-Side): Two angles and a non-included side must be congruent.
SAS (Side-Angle-Side): Two sides and the included angle must be congruent.
SSA (Side-Side-Angle): Not a valid congruence postulate.

Step-by-Step Solution:
Given congruent parts:
∠CAB ≅ ∠DAB
AC ≅ AD
AB ≅ AB
∠ACB ≅ ∠ADB
Check which congruence postulates apply:
ASA: ∠CAB, AC, and ∠ACB satisfy ASA.
AAS: ∠CAB, ∠ACB, and AB (non-included side) satisfy AAS.
SAS: AC, ∠CAB, AB satisfy SAS.
SSA: Not valid for proving triangle...