Parallel

Pronunciation: /ˈpær əˌlɛl/ ?
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Manipulative 1: Parallel lines. Created with GeoGebra.

In Euclidean geometry, two coplanar lines are parallel if they do not intersect.[1] In metric geometries, parallel lines have the same slope. Since two lines with the same slope have the same rate of change, for any change in x corresponds to an identical change in y. This means that the lines will always be the same distance apart and will never intersect. Click on the blue points in manipulative 1 and drag them to change the figure.

Transversals of Parallel Lines

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Manipulative 2: Transversal of parallel lines. Created with GeoGebra.

When two lines are parallel, a transversal of the two lines intersects each of the lines so that corresponding angles are equal.[2] Click on the blue points in manipulative 2 and drag them to change the figure. No matter how the figure is changed, corresponding angles are still equal.

References

  1. parallel. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=parallel&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 11. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/11/mode/1up.
  3. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pg 13. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-30). http://www.archive.org/stream/elementsofconstr00noetrich#page/13/mode/1up/search/transversal.
  4. transversal. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=parallel&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  5. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 15. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.allmathwords.org/article.aspx?lang=en&id=Parallel.

Cite this article as:


Parallel. 2009-12-30. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/parallel.html.

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Revision History


2009-12-30: Added "References" (McAdams, David.)
2008-10-23: Initial version (McAdams, David.)

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