# 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 |