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Question -

The side AB of aparallelogram ABCD is produced to any point P. A line through A and parallel toCP meets CB produced at Q and then parallelogram PBQR is completed (see thefollowing figure). Show that

ar (ABCD) = ar (PBQR).

[Hint:Join AC and PQ. Now compare area (ACQ) and area (APQ)]



Answer -

Let us join AC and PQ.

ΔACQ and ΔAQP are on thesame base AQ and between the same parallels AQ and CP.

Area (ΔACQ) = Area (ΔAPQ)

Area (ΔACQ) − Area (ΔABQ) = Area (ΔAPQ) − Area (ΔABQ)

Area (ΔABC) = Area (ΔQBP) … (1)

Since AC and PQ arediagonals of parallelograms ABCD and PBQR respectively,

Area (ΔABC) = Area (ABCD) … (2)

Area (ΔQBP) = Area (PBQR) … (3)

From equations (1), (2),and (3), we obtain

Area (ABCD) = Area (PBQR)

Area(ABCD) = Area (PBQR)

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