Question

If $l,m,n$ are three lines such that $l||m$ and $n\perp l,$ prove that $n\perp m.$

Answer 1

Given $l||m\text{and}n\perp l$

Since $l||m$ and $n$ intersects lines $l$ and $m$ at $G$ and $H$ respectively

$\therefore \angle 1=\angle 2$ (Corresponding angles)
$\Rightarrow \angle 2={90}^{\circ }$

Hence, $n\perp m.$