1.

In figure, ABCD and ABEF are parallelograms. Prove that CDFE is also a parallelogram.

Answer»

∵ ABCD is a parallelogram

∴ AB = DC

and AB || DC …(i)

Reason: Opposite sides of a parallelogram are equal and parallel. 

Again ABEF is a parallelogram

⇒ AB = FE

and AB || FE …(ii)

From (i) and (ii)

DC = FE and DC || FE

Therefore, CDFE is a parallelogram.

Hence proved.



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