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).
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)
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- Theorem: Parallelograms on the Same Base and Between the Same Parallels.