Question

Diagonals AC and BD of trapezium ABCD with AB||DC intersect at O.
Prove that ar(AOD) = ar(BOC).

Answer 1

Answer:

Refer to the attachment❤

Answer 2

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Two Triangles on the same base and between the same parallels are equal in area.

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Given: Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O.

To Prove:-

ar (AOD) = ar (BOC).

Proof:-

Here,△DAC and △DBC lie on the same base DC and between the same parallels AB and CD.

∴ ar(△DAC) = ar(△DBC)

ar(△DAC) − ar(△DOC) =ar(△DBC) − ar(△DOC)

[On subtracting ar(△DOC) from both sides]

ar(△AOD) = ar(△BOC)

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