Final answer:
Triangle ABC is congruent to triangle DBE by the SAS congruence postulate, given that AC is parallel to DE and B is the midpoint of AD and CE.
Step-by-step explanation:
To prove that triangle ABC is congruent to triangle DBE with the given that AC is parallel to DE and B is the midpoint of both AD and CE, we can use the congruence postulate Side-Angle-Side (SAS). Firstly, since B is the midpoint of AD and CE, we have AB = BD and BC = BE. Because AC is parallel to DE and they are intercepted by transversals AB and BC, the alternate interior angles ∠ABC and ∠DBE are equal. With AB = BD, BC = BE, and ∠ABC = ∠DBE, we can conclude that triangle ABC is congruent to triangle DBE by the SAS postulate.