Geometry

Question Analysis
This question involves proving the congruence of △ABD and △ACD using a triangle congruence postulate.
The main focus is on identifying the given information and selecting the correct postulate.

Key Concept Explanation
The AAS (Angle-Angle-Side) Congruence Postulate states that if two angles and a non-included side in one triangle are congruent to two angles and a corresponding non-included side in another triangle, then the two triangles are congruent.

Step-by-Step Solution
Given Angles:
∠ABD ≅ ∠ACD (marked in the diagram).
∠BAD ≅ ∠CAD (marked in the diagram).
Given Side:
AD is a common side to both triangles, so AD ≅ AD by the Reflexive Property.
Postulate Used:
We have two angles (∠ABD ≅ ∠ACD and ∠BAD ≅ ∠CAD) and a non-included side (AD).
This follows the AAS Congruence Postulate.

Option Analysis
HL (Hypotenuse-Leg): Incorrect, because there is no right angle given.
SAS (Side-Ang...