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. (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