Which congruence theorem can be used to prove △ BDA ≌ △ BDC ?

Step 1: Define the Problem

Identify the congruence theorem that can be used to prove that triangles $\triangle BDA$ and $\triangle BDC$ are congruent.

Step 2: Break Down the Problem

1. Identify the shared side or angle between the two triangles.
2. Determine if there are any other sides or angles that are equal between the two triangles.

Step 3: Apply Relevant Concepts

• Side-Side-Side (SSS) Congruence Theorem: If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.

Step 4: Analysis, Verify and Summarize

• Shared Side: Both triangles share side $BD$.
• Additional Information Needed: Check if there are any other sides or angles that are equal between the two triangles.

Assuming $\angle BDA = \angle BDC$ and $AD = DC$, the SAS Congruence Theorem can be applied.

Final Answer

The Side-Angle-Side (SAS) Congruence Theorem can be used to prove $\triangle BDA \equiv \triangle BDC$.