Question

Diagonals AC and BD of a trapezium Abcd with Ab|| DC interest each other at O . Prove that ar ( AoB ) = ar (CoD)

Answer 1

Given that ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O.

To prove: Area (AOD) = Area (BOC)

Proof: ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.

∴Area (ΔADC) = Area (ΔBDC) [triangles on the same base and between same parallel are equal in area]

Subtract Area (ΔDOC) from both side

Area (ΔADC) – Area (ΔDOC) = Area (ΔBDC) – Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC)

Hence proved.