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47.. question is prove that llgram on same base and between the equal parallels are equal in area
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Given : Two parallelograms ABCD & EFCD, that have the same base CD & lie between same parallels AF & CD.
To Prove : r (ABCD) = r (EFCD)
Proof : Since opposite sides of parallelogram are parallel
Also, AD = BC
In AED and BFC
DAB = CBF
DEA = CFE
AD = BC
AED BFC AED BFC Hence, r ( AED) = r ( BFC) Now, r (ABCD) = r ( ADE) + r(EBCD) = r ( BFC) + r (EBCD) = r ( EFCD) Hence, proved
To Prove : r (ABCD) = r (EFCD)
Proof : Since opposite sides of parallelogram are parallel
Also, AD = BC
In AED and BFC
DAB = CBF
DEA = CFE
AD = BC
AED BFC AED BFC Hence, r ( AED) = r ( BFC) Now, r (ABCD) = r ( ADE) + r(EBCD) = r ( BFC) + r (EBCD) = r ( EFCD) Hence, proved
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