`If a line is drawn to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

Explanation

Given D E | B C

In triangle A D E and A B C

`angle D A E=angle B A C` (common argle)

`angle A D E=angle A B C `[because D E | B C therefore correaponding anglas are equal ]

`angle A B D=angle A C B`

therefore triangle` A D E sim A A B C`

Hence `frac{A D}{A B}=
frac{A E}{A C}` (in similar triangle, corresponcing sides are in szme ratio)

...