We are asked which postulate or theorem we could use to prove the triangles are congruent. We will start by labeling the vertices in the given diagram.
Looking at the given markings, we can see that ∠ CAB and ∠ CDB are congruent as well as ∠ BCA and ∠ BCD. Additionally, both triangles share a common side BC that is congruent to itself by the Reflexive Property of Congruence.
∠ CAB ≅ ∠ CDB
∠ BCA ≅ ∠ BCD
BC ≅ BC
Therefore, two angles and the included side of △ABC are congruent to the corresponding two angles and the included side of △CBD. Consequently, we can conclude that those triangles are congruent by the Angle-Side-Angle (ASA) Congruence Theorem.
