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# parallellism in Euclidean plane

Two distinct lines in the Euclidean plane are parallel to each other if and only if they do not intersect, i.e. if they have no common point. By convention, a line is parallel to itself.

The parallelism of $l$ and $m$ is denoted

$l\parallel m.$ |

Parallelism is an equivalence relation on the set of the lines of the plane. Moreover, two nonvertical lines are parallel if and only if they have the same slope. Thus, slope is a natural way of determining the equivalence classes of lines of the plane.

Defines:

parallel, parallel lines, parallelism

Keywords:

Euclidean geometry

Related:

Slope, ParallelPostulate, ParallelCurve, PerpendicularityInEuclideanPlane

Synonym:

parallelism, parallelism in plane, parallelism of lines

Type of Math Object:

Definition

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

51-01*no label found*

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clarify/amend by Wkbj79 ✓