## ::Parallel (geometry)

### ::concepts

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

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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