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


Best Answer

Sol: Given : Parallelogram ABCD and ABEF are on the same base AB and between the same parallels AB and CF.

To Prove : ar. (ABCD) = ar. (ABEF)

To Prove : ar. (ABCD) = ar. (ABEF)

Proof : In DADF and DBCE, we have

AF = BE

AD = BC 

and      ÐDAF = ÐCBE                               

DADF @ DBCE                                                [By SAS Congruence]                               

 ar. (DADF) = ar. (DBCE)                     [Congruence area axiom]

Adding ar.(quadrilateral ABED) to both sides, we get

ar. (DADF) + ar.(quadrilateral ABED) = ar.(quadrilateral ABED) + ar DBCE

ar. ||gm ABEF = ar. ||gm ABCD                       [Area addition axiom]  

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