Given :For a quadrilateral ABCD, diagonals AC and BD intersect at O. And ar(ΔAOD) = ar(ΔBOC)
To prove: ABCD is a trapezium.
Adding ar(ODC) on both sides , ar(ΔAOD) + ar(ΔODC) = ar(ΔBOC) + ar(ΔODC)
→ar(ΔADC) = ar(ΔBDC)
→1/2 × DC × AL = 1/2 × DC × BH
→AL = BH
→AB || DC
So, ABCD is a trapezium.