Question

ABCD is a trapezium in which AB parallel DC and its diagonal AC and BD intersect at O. Prove that area of triangle AOD= area of triangle BOC

Answer 1

We know
ar(ADC) = ar(BCD) [ Δs on the same base and between same parallels]

Now, by subtracting ar(DOC) from both the sides,
ar(ADC) - ar(DOC) = ar(BCD) - ar(DOC)
ar(AOD) = ar(BOC).