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Question

Diagonals AC and BD of a trapezium ABCD with AB  DC intersect each other at O.
Prove that ar (AOD) = ar (BOC).  [1 MARK]


Solution

Concept : 0.5 Mark
Application : 0.5 Mark



 

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

 Area (DAC) = Area (DBC)

 Area (DAC) − Area (DOC) = Area (DBC) − Area (DOC)  [ subtracting Area (DOC) on both sides]

 Area (AOD) = Area (BOC)

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