Geometry

Question Analysis
This question involves proving the congruence of △ABC and △DBC using a triangle congruence postulate.
The main focus is on determining whether the given side is included or non-included between the two angles.

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
Identify Given Information:
∠ABC ≅ ∠DBC (congruent angles).
∠BAC ≅ ∠BDC (congruent angles).
BC is a common side, meaning BC ≅ BC by the Reflexive Property.
Determine Triangle Congruence Postulate:
We have two angles and a non-included side.
This follows the AAS Congruence Postulate because the side is not between the two given angles.

Option Analysis
Option A (ASA): Incorrect, because the given side is not included between the two angles.
Option B (AAS): Correct, since we have two angles and a non-included side congruent.
Option C (SAS): Incorrect, because the ...