Question

In quadrilateral ABCD, diagonals AC and BD bisect one another:

What statement is used to prove that quadrilateral ABCD is a parallelogram?

Angles BAD and ADC are congruent.

Corresponding angles BCD and CDA are supplementary.

Sides CD and DA are congruent.

Vertical angles BPA and DPC are congruent.

Answer 1

Your answer is D!hope i helped

Answer 2

Correct answer is D.

AP = PC
BP = PD

`\angle{BPA}=\angle{DPC}`

`\triangle{ABP} \cong \triangle{DPC} \Rightarrow AB=CD`

AP = PC
BP = PD

`\angle{APD}=\angle{CPB}`

`\triangle{APD} \cong \triangle{CPB} \Rightarrow AD=CB`

The opposite sides of quadrilateral ABCD are equal. Therefore, quadrilateral ABCD is a parallelogram.