Diagonals AC and BD of a trapezium ABCD with AB ∥ DC intersect each other at O.then, ar (△AOD) =
Area (△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) |