Question

Thales theorem and inverse of Thales theorem too..​

Answer 1

Answer:

Step-by-step explanation:

Let us now state the Basic Proportionality Theorem ( thale's ) which is as follows:

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

converse of thale : According to this theorem, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Answer 2

Answer:

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

Given :- In triangle ABC , DE || BC.

To prove :- AB/DB = AE/EC.

Construction :- Join BE & CD.

drawn DM | AC & EN | AB.

Proof :- ar (triangleADE) = 1/2×base×height.

ar(triangleADE) = 1/2 AD×EN.

& ar(triangleBDE) = 1/2 EC×DM.

& ar(triangle ADE) = 1/2 AE×DM.

therefore ar(DEC) = 1/2×EC×DM.

ar(ADE) / ar(BDE)

= 1/2×AD×EN / 1/2×BD×EN

= AD/BD____(1)

ar(ADE) / ar(DEC)

= 1/2×AE×DM / 1/2×EC×DM

= AE/EC____(2)

ar(BDE) = ar(DEC) {same base DE & DE||BC}

from equation (1) , (2) , (3)

AD/BD = AE/EC.

HENCE PROVED.✔