Q: 5     In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

            (i)   \small ar(PQRS)=ar(ABRS)
           (ii)  \small ar(AXS)=\frac{1}{2}ar(PQRS)

            

Answers (1)


(i) Parallelogram PQRS and ABRS are on the same base RS and between the same parallels RS and PB.
Therefore,  \small ar(PQRS)=ar(ABRS)............(i)
Hence proved

(ii) \DeltaAXS and ||gm ABRS are on the same base AS and between same parallels AS and RB.
Therefore, ar (\DeltaAXS) = 1/2 . ar(||gm ABRS)............(ii)

Now, from equation (i) and equation (ii), we get

\small ar(AXS)=\frac{1}{2}ar(PQRS)

Hence proved.

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