Parallel

Pronunciation: /ˈpær əˌlɛl/ Explain
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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. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 11. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 1/2/2010. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/11/mode/1up. Buy the book
  2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 13. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/31/2009. http://www.archive.org/stream/elementsofconstr00noetrich#page/13/mode/1up/search/transversal. Buy the book
  3. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 15. D. Van Nostrand Company. 1908. Last Accessed 1/2/2010. http://www.allmathwords.org/article.aspx?lang=en&id=Parallel. Buy the book

Cite this article as:

McAdams, David E. Parallel. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/parallel.html.

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Revision History

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

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