parallellism in Euclidean plane

Two distinct lines in the Euclidean planeMathworldPlanetmath are parallelMathworldPlanetmathPlanetmathPlanetmath 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


Parallelism is an equivalence relationMathworldPlanetmath 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 classesMathworldPlanetmath 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