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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.

Verified Answer :

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.

Your answer is D!hope i helped

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