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  • P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

Q : 3      P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that \small ar(APB)=ar(BCQ).

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We have, 
ABCD is a parallelogram, therefore AB || CD and BC || AD.


Now,  \DeltaAPB and ||gm ABCD are on the same base AB and between two parallels AB and DC.
Therefore, ar  (\DeltaAPB) = 1/2 . ar(||gm ABCD)...........(i)

Also, \DeltaBQC and ||gm ABCD are on the same base BC and between two parallels BC and AD.
Therefore, ar(\DeltaBQC) = 1/2 . ar(||gmABCD)...........(ii)

From eq(i) and eq (ii),  we get,
ar  (\DeltaAPB) =  ar(\DeltaBQC)
Hence proved.

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manish

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