<P> In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel . By extension, a line and a plane, or two planes, in three - dimensional Euclidean space that do not share a point are said to be parallel . However, two lines in three - dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines . Parallel planes are planes in the same three - dimensional space that never meet . </P> <P> Parallel lines are the subject of Euclid's parallel postulate . Parallelism is primarily a property of affine geometries and Euclidean geometry is a special instance of this type of geometry . In some other geometries, such as hyperbolic geometry, lines can have analogous properties that are referred to as parallelism . </P>

Two lines in the same plane that do not intersect are called