Question

Show that 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

Given $\Rightarrow XY||BC$

To Prove $\Rightarrow \frac{AX}{AB}=\frac{AY}{AC}$

Proof $\Rightarrow XY||BC$

In $△AXY$ and $△ABC$,

$\begin{array}{c}\angle AXY=\angle ABC\\ \angle AYX=\angle ACB\end{array}\}$ corresponding angles

Hence, $△AXY\sim △ABC$ (By $AA$ criterion)

As we know that, corresponding parts of the similar triangle are proportional,

Hence proved, $\frac{AX}{AB}=\frac{AY}{AC}$