1.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD show that ar(ΔAPB)=ar Δ(BQC).

Answer»

If a parallelogram and a triangle are on the same base and between the same parallels then area of the triangle is half the area of the parallelogram.


==========================================================


Given: In parallelogram ABCD, P & Q any two POINTS lying on the sides DC and AD.

To show: ar (APB) = ar (BQC).

Proof:

Here, ΔAPB and ||gm ABCD stands on the same base AB and lie between same parallel AB and DC.

Therefore,

ar(ΔAPB) = 1/2 ar(||gm ABCD) — (i)


Similarly,

Parallelogram ABCD and ∆BQC stand on the same base BC and lie between the same parallel BC and AD.

ar(ΔBQC) = 1/2 ar(||gm ABCD) — (II)


From eq (i) and (ii),we have

ar(ΔAPB) = ar(ΔBQC)


HOPE this will help you...


Discussion

No Comment Found

Related InterviewSolutions