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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.

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HomertheGenius
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 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.

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