# parallellism in Euclidean plane

Two distinct lines in the Euclidean plane are to each other if and only if they do not intersect, i.e. (http://planetmath.org/Ie) 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.

 Title parallellism in Euclidean plane Canonical name ParallellismInEuclideanPlane Date of creation 2013-03-22 17:12:38 Last modified on 2013-03-22 17:12:38 Owner pahio (2872) Last modified by pahio (2872) Numerical id 10 Author pahio (2872) Entry type Definition Classification msc 51-01 Synonym parallelism Synonym parallelism in plane Synonym parallelism of lines Related topic Slope Related topic ParallelPostulate Related topic ParallelCurve Related topic PerpendicularityInEuclideanPlane Defines parallel Defines parallel lines Defines parallelism