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TortureMan

D. the final one, the one you currently have answered is the correct one, this is because a parallelogram, like this one, requires that the triangles on either side must be congruent in order for this to be true.

vijayhalder031

Triangles BPA and DPC are congruent is the statement used to prove the quadrilateral is parallellogram.

What is Parallellgram?

  • It is a Quadrilateral in which opposite sides are parallel and equal to each other.

How to solve the problem?

The problem can be solved by following steps.

  • It is given that diagonals AC and BD bisects each other.
  • We need to find the correct statement.

BP=PD and CP=AP

In ∆BPA and ∆DPC

AP=CP (side)

PD = BP (side)

angle APB = angle CPD (Vertically opposite angles)

By SAS Criteria ∆BPA is congruent to ∆DPC

Therefore ABCD is a parallelogram.

Hence the correct statement is Triangles BPA and DPC are congruent

Learn more about parallelogram here

https://brainly.com/question/20526916

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