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Question

Prove that parallelogram on the same base and between the same parallels are equal in area.

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Solution



Given: The parallelograms ABCD and ABEF be on the same base AB and between same parallels AB and FC.

​To prove: ar(ABCD) = ar(ABEF)

Proof:

As, CD=AB Opposite sides of parallelogram ABCDAnd, FE=AB Opposite sides of parallelogram ABEFSo, FE=CDFE+ED=CD+EDFD=CE .....iNow,In ADF and BCE,AD=BC Opposite sides of parallelogram ABCDAF=BE Opposite sides of parallelogram ABEFDF=CE From iSo, by SSS congruencyADFBCEarADF=arBCE Congruent triangles are equal in areaarABCF-arADF=arABCF-arBCE arABCD=arABEF


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