Question

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 1

Option D.

Explanation:

In the figure attached, Diagonals AC and BD are bisecting each other at a point P.

That means AP ≅ CP and DP ≅ BP

We have to prove : AB ≅ DC and AB ║ DC

Proof : In triangles BPA and CPD,

AP ≅ CP

DP ≅ BP

∠ APB ≅ ∠DPC [vertically opposite angles]

Therefore, by postulate SAS [Side-Angle-Side]

ΔBCP ≅ ΔCDP

Option D. will be the answer.