Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC)

It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD

Area (ΔDAC) = Area (ΔDBC)

Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC)