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P and Q are any two points lying on the...

P and Q are any two points lying on the sides DC and AD respectively of a parallelogramABCD. Show that `a r\ (A P B)\ =\ a r\ (B Q C)`.

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Draw `PM bot AB and QN bot BC`
`ar(DeltaAPB) = (1)/(2) xx (AB xx PM) = (1)/(2) xx ar (||gm ABCD)`....(1)
`ar(DeltaBQC) = (1)/(2) xx (BC xx QN) = (1)/(2) xx ar (||gm ABCD)`...(2)
`:.` From (1) and (2), we get
`ar(DeltaAPB) = ar(DeltaBQC)`
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