Question

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

Answer 1

Answer:

Given Two lines m and n are parallel and another two lines p and q are respectively perpendicular to m and n.

i.e., p ⊥ m, p ⊥ n, q ⊥ m, q ⊥ n

To prove p||g

Proof Since, m || n and p is perpendicular to m and n.

So, sum of two interior angles is supplementary.

We know that, if a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

Hence, p||g.