Question

Prove the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures.

Answer 1

AB and DC are parallel.
Therefore the angles marked 1 are equal (alternate angles)
and angles marked 2 are equal (alternate angles)
AB = CD (opposite sides of parallelogram are congruent)
Therefore, triangles OAB and OCD are congruent (ASA postulate)
Therefore OB = OD (CPCTC) and
OA = OC (CPCTC)

Therefore, the diagonals of a parallelogram bisect one another.