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).
Solution:
ABCD is a parallelogram. P is the point on side CD and Q is the point on side AD.
We need to show that ar(APB)=ar(BQC)
We can note that parallelogram ABCD and
are on the same base BC and between the same parallels BC and AD. It means that
(1)
In the same way, parallelogram ABCD and
are on the same base AB and between the same parallels AB and CD. It means that
(2)
From (1) and (2), we can say that
Hence Proved
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