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6.EXAMPLE 12In the adjoining figure, PORS and PABC aretwo parallelograms of equal area. Prove thatQC|| BR.Let BC and QR intersect at O.Join BQ, QC, CR and RB.OLUTION |
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Answer» Let QR and BC intersect at O.Join CQ, QB, BR and RC.ar(//gm PQRS) = ar(//gm PABC)⇒ ar(//gm PQOC) + ar(//gm CORS) = ar(//gm PQOC ) + ar(//gm QABO)⇒ ar(//gm CORS) = ar(//gm QABO)⇒1/2 ar(//gm CORS) = 1/2 ar(//gm QABO)⇒ar (ΔCOR) = ar (ΔQOB)⇒ar (ΔCOR) + ar (ΔCQO) = ar (ΔQOB) + ar (ΔCQO)⇒ar (ΔCQR) = ar (ΔCQB) ΔCQR and ΔCQB are on the same base CQ and have equal areas. Therefore, ΔCQR and ΔCQB lie between the same parallels QC and BR.Hence, QC // BR |
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