Final answer:
To prove ΔABD ≅ ΔCDB, the Angle-Angle-Side (AAS) congruence theorem is used, as two angles and a non-included side are congruent in each triangle.
Step-by-step explanation:
The concerned student's question is about proving the congruence of two triangles, ΔABD and ΔCDB, using a theorem or postulate. Given that ab is parallel to dc and a is equal to c, we can utilize the Angle-Angle-Side (AAS) congruence theorem to prove that the two triangles are congruent. This theorem states that two triangles are congruent if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle.
By the given, we already have two pairs of congruent angles (angle A is congruent to angle C, angle B is congruent to angle D due to parallel lines and the Alternate Interior Angles Theorem). Additionally, side AD in ΔABD is equal to side CB in ΔCDB since a is equal to c. Therefore, the answer is C. AAS to prove that the two triangles are congruent.