Question

In quadrilateral ABCD, diagonals AC and BD bisect one another: What statement is used to prove that quadrilateral ABCD is a parallelogram?
A) Segment AP is congruent to segment CP.

B) Segment BP is congruent to segment AP

C) Sides AB and BC are congruent.

D) Triangles BCP and CDP are congruent.

Answer 1

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.

Answer 2

The correct answer is:

A) AP is congruent to CP.

Explanation:

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.