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CBSE Class 9 Answered

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that area ABCD = area PBQR.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

Join AC and PQ. ACQ and APQ lie on the same base AQ and between the same parallels CP and AQ

area ACQ = area APQ

area ACQ - area ABQ = area APQ - area ABQ

area ABC = area PBQ

2 area ABC = 2 area PBQ … (i)

AC is the diagonal of parallelogram ABCD.

area ABC = area ADC = area ABCD

area ABCD = 2 area ABC ... (ii)

Similarly, area PBQR = 2 area PBQ ... (iii)

From (i), (ii) and (iii),

area ABCD = area PBQR

Answered by | 04 Jun, 2014, 03:23: PM

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