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'parallellism in Euclidean plane'
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| Title of object: |
parallellism in Euclidean plane |
| Canonical Name: |
ParallellismInEuclideanPlane |
| Type: |
Definition |
| Created on: |
2007-06-05 13:32:04 |
| Modified on: |
2007-08-28 04:42:51 |
| Classification: |
msc:51-01 |
| Keywords: |
Euclidean geometry |
| Defines: |
parallel, parallel lines, parallelism |
| Synonyms: |
parallellism in Euclidean plane=parallelism
parallellism in Euclidean plane=parallelism in plane
parallellism in Euclidean plane=parallelism of lines |
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Content:
Two distinct lines in the Euclidean plane are {\em parallel} to each other if and only if they do not intersect, \PMlinkname{i.e.}{Ie} if they have no common point. By convention, a line is parallel to itself.
The {\em 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. |
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