Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to intersect, but also maintain a constant separation between points closest to each other on the two lines. Therefore, parallel lines in three-space lie in a single plane. Lines in three-space which are not parallel but do not intersect are called skew lines.

café wall illusion | coplanar | intersecting lines | parallel | parallel curves | parallel line and plane | parallel planes | parallel postulate | perpendicular | Ponzo's illusion | Proclus' axiom | skew lines | Zöllner's illusion