# Parallel (geometry)

## Relation used in geometry / From Wikipedia, the free encyclopedia

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In geometry, **parallel lines** are coplanar infinite straight lines that do not intersect at any point. **Parallel planes** are planes in the same three-dimensional space that never meet. *Parallel curves* are curves that do not touch each other or intersect and keep a fixed minimum distance. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However, two noncoplanar lines are called *skew lines*. Line segments and Euclidean vectors are parallel if they have the same direction (not necessarily the same length).

Parallel lines are the subject of Euclid's parallel postulate.^{[1]} 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.