Final answer:
To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. Given that AD is parallel to BC, and ∠ABD is congruent to ∠CDB, we can use the alternate interior angles theorem to infer that AB is parallel to CD.
Step-by-step explanation:
To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. Given that AD is parallel to BC, and ∠ABD is congruent to ∠CDB, we can use the alternate interior angles theorem to infer that AB is parallel to CD. Similarly, since BC is parallel to AD, and ∠CDB is congruent to ∠ABD, we can use the alternate interior angles theorem again to infer that BC is parallel to AD. Thus, all pairs of opposite sides are parallel, and we can conclude that ABCD is a parallelogram.