Question

State an prove Thales Theorem.​

Answer 1

Answer:

The Thales theorem states that: If three points A, B, and C lie on the circumference of a circle, whereby the line AC is the diameter of the circle, then the angle ∠ABC is a right angle (90°).

Explanation:

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Answer 2

Answer:

Explanation:

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