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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).

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#### Solution

It can be observed that ΔBQC and parallelogram ABCD lie on the same base BC and these are between the same parallel lines AD and BC.

∴Area (ΔBQC) = 1/2Area (ABCD) ... (1)

Similarly, ΔAPB and parallelogram ABCD lie on the same base AB and between the same parallel lines AB and DC.

∴ Area (ΔAPB) = 1/2Area (ABCD) ... (2)

From equation (1) and (2), we obtain

Area (ΔBQC) = Area (ΔAPB)

Concept: Theorem: Parallelograms on the Same Base and Between the Same Parallels.

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