Question

I'm very stuck on this problem, mainly because of how restricted the selection of proofs is, and if you can help or give ideas I would really appreciate just listening to your thoughts on the question, thank you!

Answer 1

Check the picture below.

so in the parallelogram, the two triangles split by the side AC are congruents as you can see there by AAS, that means their sides and angles are congruent, that also includes the exterior angles.

since the exterior angles are also congruent, we can extend lines BC and AD as you see there in green and run an exterior angle at vertices A and C, since those two exterior angles are congruent and are also alternate interior ones, voila! it must be that BC || AD.