Question

Two lines are respectively perpendicular to two parallel lines Show that they are parallel to each other.

Answer 1

ANSWER:
Let m and n be the two parallel lines perpendicular to the line l.
Since, l is perpendicular to m,
$\angle 1={90}^{\circ }$
Also, since l ​ is perpendicular to m,
$\angle 2={90}^{\circ }$
Therefore, $\angle 1=\angle 2$
This implies that the corresponding angles are equal.
Therefore, the lines m and n are parallel to each other.