As you will see below, if two lines do not intersect, they are not always parallel. Skew lines and parallel lines are different. Though skew and parallel both imply non intersecting lines, parallel is the special case where the two lines are also in the same plane ...

I have attached two pictures below:

The first one is depicting two parallel lines AB and CD.Parallel lines are lines that are in the same plane but do not intersect. AB and CD are both in the plane ABCD and do not intersect therefore they are parallel.

The second picture is of skew lines TR and AC. Though they do not intersect, they are not in the same plane. It is not possible to draw a plane that could have both lines TR and AC in it.Lines that do not intersect and are not in a shared plane are skew lines.

Math Guru