In the adjoining figure, ABCD is a ||gm whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) =12ar(ABCD).

In the adjoining figure, ABCD is a ||gm whose diagonals AC and BD inte

1.	In the adjoining figure, ABCD is a \|\|gm whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) =12ar(ABCD).
Answer» In the adjoining figure, ABCD is a $\| \|^{g m}$ whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) $= \frac{1}{2}$ ar(ABCD).