Question

Proof of basic proportionality theorem ​

Answer 1

`\boxed{ \sf \: Basic \: Proportionality \: Theorem \: (BPT)}`

This theorem states that if a line is drawn parallel || to one side of a triangle ∆ to intersect the other 2 sides in distinct points, the other 2 sides are divided in the same ratio.

From the figure, with the help of this proof, we can see that :-

`\sf \: (AD)/(AE) = (AE)/(EC) \\`

Refer to the attached pictures for the proof & the figure.

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Hope it helps.

RainbowSalt2222

Answer 2

Basic proportionality theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio. and DE intersects AB and AC at D and E respectively. ... Hence we can say that the basic proportionality theorem is proved.