The following figure can be drawn from the given details.

Here, we have

l and m are two lines perpendicular to the same line n.

⇒ ∠lan = ∠mbn = 90° - - - - (i)

Now, we can see that n is a transversal intersecting two lines l and m at points a and b, such that,

the corresponding angles, ∠lan = ∠mbn and are 90° each.

Since, the corresponding angles between two lines are equal when a transversal intersects these two lines at two different points, the two lines are parallel to each other.

Thus, the lines l and m are parallel to each other, not perpendicular.