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

Q : 10    Diagonals AC and BD of a trapezium ABCD with  \small AB\parallel DC  intersect each other at O. Prove that  \small ar(AOD)=ar(BOC).
 

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We have a trapezium ABCD such that AB || CD and it's diagonals AC and BD intersect each other at O 
\DeltaABD and \Delta ABC are on the same base AB and between same parallels AB and CD 
\therefore ar(\DeltaABD) = ar (\DeltaABC)

Now, subtracting \DeltaAOB from both sides we get

ar (\Delta AOD) = ar (\Delta BOC)

Hence proved.

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manish

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