::Parallel (geometry)


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Line art drawing of parallel lines and curves.

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