Question

Two straight lines are perpendicular on two parallel lines. Show that these two straight lines are parallel.

Answer 1

Suppose $l$ and $m$ re two parallel lines and $p$ & $q$ are two lines perpendicular to $l$ and $m$

$\angle ADC+\angle BCD={90}^0+{90}^0$

$\Rightarrow \angle ADC+\angle BCD={180}^0$

Since $p$ and $q$ are two lines and $DC$ is a transversal angles is ${180}^0$

therefore $p\parallel q$

proved