Question

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

Answer 1

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