Are lines that are perpendicular to the same line parallel?

Question

Sometimes, always, or never?

If sometimes, explain your answer.

Answer 1

It depends on if you a working in two dimensions or three and if you are working in Euclidean geometry or non-Euclidean geometry.

In Euclidean plane geometry in two dimensions if the two lines are perpendicular to the same line through two distinct points on that line, they will be parallel.

If you are in three dimensions going through two distinct points, they could be parallel if lying in the same plane or not if not in the same plane.

In non-Euclidean elliptic geometry on the surface of a sphere they would always intersect like longitude lines as they are perpendicular to the equator or latitude lines at different points and all intersect at the north and south poles.
or
In non-Euclidean hyperbolic geometry on the surface of a hyperboloid they would be parallel using an analogy to latitude and longitude lines.

Answer 2

alwayz, perpendicular is a line at a right angel to another line, if there are two line perp to the same line they will never touch, witch means they are paralel

Answer 3

If line a is perpendicular to line b, then line c has to be parallel to line a if it is perpendicular to line b....always.

Answer 4

Sometimes, if they lie in the same plane. If they lie in different planes, they arenot parallel, and are called skew lines.

Answer 5

Yes. Always.