Question

In the given figure, ABCD is a trapezium in which AB || DC and diagonals AC and BD intersect at O. Prove that ar(∆AOD) = ar(∆BOC).

Answer 1

In trapezium ABCD, AB || DC and AC and BD are the diagonals which intersect at O.
As ​∆ACD and ∆BCD lie on the same base and between the same parallel lines.
∴​ ar(∆ACD) = ar(∆BCD) ​
⇒ ar(∆ACD) − ar(∆COD) = ar(∆BCD) − ar(∆COD)​
Hence, ar(∆AOD) = ar(∆BOC)