1.

State and prove thale's theorm

Answer»

Step-by-step explanation:

Given,

A triangle ABC in which DE// BC and DE intersects AB and AC at D and E respectively.

To prove ,

AD/DB = AE/EC.

construction,

Join BE and CD .

DRAW EL perpendicular AB and DM perpendicular AC .

proof,

we have,

ar ( ADE) = 1/2 × AD × EL

and , ar( DBE ) 1/2 × DB × EL

therefore, ar( ADE) / ar ( DBE) = 1/2 × AD × EL / 1/2 × DB × EL = AD/DB . --------- 1

similarly,

ar(ADE) / ar( ECD) = 1/2 × AE × DM / 1/2 × EC × DM = AE/EC . -------- 2

Now,

triangle DBE and triangle ECD being on the same base DE and between the parallels DE and BC , we have

ar( DBE) = ar( ECD ) --------- 3

from 1 ,2 and 3 , we have, AD / DB = AE / EC .

I have not drawn the drawing but you can easily do it from the solution given....


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