## ::Parallel (geometry)

### ::concepts

Lines::parallel Geometry::plane Point::''l'' Space::''m'' Common::distance ''a''::through

{{#invoke:redirect hatnote|redirect}}

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.

Parallel lines are the subject of Euclid's parallel postulate.<ref>Although this postulate only refers to when lines meet, it is needed to prove the uniqueness of parallel lines in the sense of Playfair's axiom.</ref> Parallelism is primarily a property of affine geometries and Euclidean space is a special instance of this type of geometry. Some other spaces, such as hyperbolic space, have analogous properties that are sometimes referred to as parallelism.

**Parallel (geometry) sections**

Intro Symbol Euclidean parallelism Extension to non-Euclidean geometry Reflexive variant See also Notes References Further reading External links

PREVIOUS: Intro | NEXT: Symbol |

<< | >> |