Question

In the given figure ABC is a triangle. If $\frac{AD}{AB}=\frac{AE}{AC}$, then prove that DE || BC.

Answer 1

Given:

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

To prove that:

$DE||BC$

Proof:

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

$\angle A$ is common angle in $\Delta ADE$ and $\Delta ABC$.

$⟹\Delta ADE\sim \Delta ABC$ by $SAS$ similarity

$⟹\angle ADE=\angle ABC$ by properties of similar triangles

$\therefore DE||BC$ by property of corresponding angles for parallel lines. $\left[henceproved\right]$