Statement B is true only for a square. Statements C and D are true only for a square and a rhombus but we want to prove that quadrilateral ABCD is a parallelogram. Answer: A ) Segment AP is congruent to segment CP.
The only information we are given is that the diagonals AC and BD bisect each other at some unknown point. This means that the distance from A to this point is the same as the distance from this point to C; this gives us AP congruent to CP.