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 (see figure). Show that ar(ABCD)=ar(PBQR).
[Hint: Join AC and PQ. Now compare ar(ACQ) and ar(APQ)]
Solution:
It is given that ABCD and PBQR are two parallelograms.
We need to show that ar(ABCD)=ar(PBQR)
Construction: Join AC and PQ.
We have
(Triangles on the same base and between the same parallels are equal in area.)
(Diagonal of parallelogram divides it into two triangles of equal areas.)
Leave a Reply