Geometry

Question Analysis:
This question involves two triangles that share a common side and have an equal angle between two given sides.
The main focus is identifying the correct congruence postulate and ensuring that the angle is the included angle between the two sides.

Key Concept Explanation:
SAS Congruence Postulate: Two triangles are congruent if two pairs of corresponding sides and their included angle are equal.
Shared Sides Property: If two triangles share a side, that side is automatically equal in both triangles.

Step-by-Step Solution:
Identify Given Information:
AB = DB ✅ (corresponding sides)
∠ABC = ∠DBC ✅ (included angle is equal)
BC is a shared side ✅ (common in both triangles)
Check for SAS Conditions:
Two pairs of corresponding sides are equal:
AB = DB and BC = BC (shared side). ✅
The included angle ∠ABC=∠DBC is also equal. ✅
This satisfies SAS, proving △ABC≅△DBC. ✅

Option Analysis:
(A) Incorrect: We do not have three equal sides, so SSS does not apply. ❌
(B) Correct: The two sides and included angle satisfy SAS, proving congruence. ✅
(C) Incorrect: ASA requires two angl...