Question

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

Answer 1

Let the two lines m and n be respectively perpendicular to the two parallel lines p and q.
To prove: m is parallel to n.
Proof: Since, m is perpendicular to p
$\therefore$$\angle 1=90°$
Also, ​n is perpendicular to q
$\therefore$$\angle 3=90°$
Since p and q are parallel and m is a transversal line
$\therefore$ $\angle 2=\angle 1=90°$ [Corresponding angles]
Also, $\angle 2=\angle 3=90°$
We know that if two corresponding angles are equal then the two lines containing them must be parallel.
Therefore, the lines m and n are parallel to each other.