Prove that If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram.

Explanation

Since AC is the diagonal

`ar(/_ABC)=ar(/_ACD)`

`ar(/_ABC)+ar(/_ACD)=ar(ABCD)`

`ar(/_ABC)=1/2ar(ABCD)-(1)`

Since,BD is the diagonal

`ar(/_ABD)=ar(/_CBD)`

`ar(/_ABD)+ar(/_CBD)=ar(ABCD)`

`ar(/_ABD)=1/2ar(ABCD)-(2)`

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