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Question

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

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Solution

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.

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