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.
Two lines may or may not lie in the same plane, depending on their relationship. If the lines are parallel or intersecting, they exist in the same plane. However, if the lines are skew, meaning they do not intersect and are not parallel, they lie in different planes. Thus, whether two lines lie in the same plane is contingent on their geometric arrangement.
Parallel lines. they never intersect and lie on the same plane.parallel lines
Parallel Lines.
parallel
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