Question

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

Answer 1

Let $DE$ is parallel to $BC$.

In $△ADE$ and $△ABC,$

$\angle DAE=\angle BAC$ [Common]

$\angle ADE=\angle ABC$ [Corresponding angles]

$\angle AED=\angle ACB$ [Corresponding angles]

By using the $AAA$ criterion of similarity,

$△ADE\sim △ABC$

$\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}$

$\Rightarrow \frac{AD}{DB}=\frac{AE}{EC}$

Hence, the given statement is true.