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Pls solve bpt theorem for me urgently in easy way

Answer»

Given :- In triangle ABC, DE || BC

To Prove :- AD / BD = AE / CE

Construction :- Join DC, BE, draw DG Perpendicular to AC and EF Perpendicular to AB

Proof :-

ar (ADE) = AD × EF / 2 -----(1)

ar (BDE) = BD × EF / 2 ------(2)

On dividing equation 1 by 2, we get

ar ( ADE) / ar ( BDE) = AD / BD -------(3)


Similarly,

ar (ADE) / ar (DEC) = AE / EC ------(4)


But,

ar ( DEC) = ar ( BDE) ( They are on same base and between same PARALLEL lines)

On putting this value in equation (4), we get

ar (ADE) / ar (BDE) = AE / EC -------(5)

On comparing equation (3) and (5), we get


AD/BD = AE / EC



Hence Proved...


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