Need in quadrilateral abcd, diagonals ac and bd bisect one another: what statement is used to prove that quadrilateral abcd is a parallelogram? angles abc and bcd are congruent. sides ab and bc are congruent. triangles bpa and dpc are congruent. triangles bcp and cdp are congruent.

Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.

Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.

If P is a an intersection point of these diagonals

Then we can say that, AP=PC and BP=PD ( by the property of bisecting)

So, In quadrilateral ABCD,

Let us take two triangles,  and  .

Here, AP=PC

BP=PD,

( vertically opposite angles.)

So, By SAS postulate,

Thus AB=CD  ( CPCT).

Similarly, we can prove,

Thus, AD=BC (CPCT).

Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.

Therefore, quadrilateral ABCD is a parallelogram.

Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.

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