They usually do. But latitudes, which measure distances from the equator and which, on earth, are called the parallels of latitude, do not lie in a plane.
Parallel
Parallel Lines - Skew lines are lines that do not intersect and do not lie in the same plane. If two lines lie in the same plane they they must either intersect or they are parallel.
Parallel lines. they never intersect and lie on the same plane.parallel lines
parallel
Parallel Lines.
Parallel
Two lines can lie in one plane. For example, parallel lines are lines that intersect and lie in the same plane.
If the two lines lie in the same plane, and they do not intersect, then they are parallel. If they are not in the same plane, and do not intersect, then they are called skew lines.
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length
Parallel lines
parallel lines