Question

state and prove Thales theorem with diagram

Answer 1

$\mathfrak{\huge{\blue{\underline{\underline{ANSWER :}}}}}$

Statement: If a line is drawn parallel to one side of a triangle, to intersect the other two sides at distinct 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

$<marquee>$Hope It Will Help.❤️

Answer 2

Answer:

Proof on Thales theorem:-

If a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

Given : In ∆ABC , DE || BC and intersects AB in D and AC in E.

Construction : Join BC,CD and draw EF ┴ BA and DG ┴ CA.

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Thales's theorem states:-

If a line is drawn parallel to one side of a triangle, then it divides the other two sides in the same ratio.

This theorem is also called as basic proportionality theorem.

that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

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