Question

state and prove thales theorem​

Answer 1

Step-by-step explanation:

Statement: If a line is drawn parallel to one side of a triangle, to interest the other two sides at indistinct points, the other two sides are divided in the same ratio.

Given: - In △ABC,DE∥BC

To prove:- AD/DB = AE/EC

Construction:- BE and CD are joined. EF⊥AB and DN⊥AL

 are drawn.

Proof:-

ar(△ADE) = 1/2×AD×EF

                  =1/2×AE×DN

ar(△BDE) = 1/2×BD×EF

ar(△CDE) = 1/2×EC×DN

ar(△ADE)/ar(△BDE) = 1/2×AD×EF/1/2×BD×EF   ........(1)

ar(△ADE)/ar(△CDE) = 1/2×AE×DN/1/2×EC×DN   ........(2)

But, ar(△BDE) = ar(△CDE)    ..............(3)

 

as they are on the same base DE and DE∥BC

 from (1), (2) and (3) we get AD/DB = AE/EC

Answer 2

Answer:

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