NEED ASAP!!!!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.

Answer: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 diagonalsThen we can say that, AP=PC and BP=PD ( by the property of bisecting)So, In quadrilateral ABCD,Let us take two triangles, [tex]\triangle BPA[/tex]  and  [tex]\triangle DPC[/tex].Here, AP=PC BP=PD,[tex]\angle APB=\angle DPC[/tex] ( vertically opposite angles.)So, By SAS postulate,[tex]\triangle BPA\cong \triangle DPC[/tex]Thus AB=CD  ( CPCT).Similarly, we can prove, [tex]\triangle APD\cong \triangle BPC[/tex]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.