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)
