Parallel
Pronunciation: /ˈpær.əˌlɛl/ Explain
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Why does the length of C always equal the length of D.
 Manipulative 1  Parallel Lines Created with GeoGebra. 

In Euclidean geometry, two
coplanar
lines are parallel if they do not
intersect.^{[2]}
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.

Transversals of Parallel Lines
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Is there any way to make opposite angles different for a transversal of parallel lines?
 Manipulative 2  Parallel Lines with a Transversal 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.^{[3]}

References
 McAdams, David E.. All Math Words Dictionary, parallel. 2nd Classroom edition 201501084799968. pg 134. Life is a Story Problem LLC. January 8, 2015. Buy the book
 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 12/3/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/11/mode/1up. Buy the book
 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 12/3/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/13/mode/1up/search/transversal. Buy the book
 Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 15. D. Van Nostrand Company. 1908. Last Accessed 12/3/2018. https://www.allmathwords.org/article.aspx?lang=en&id=Parallel. Buy the book
More Information
 Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.
Cite this article as:
McAdams, David E. Parallel. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/p/parallel.html.
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Revision History
4/27/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup, updated geogebra app. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
12/30/2009: Added "References". (
McAdams, David E.)
10/23/2008: Initial version. (
McAdams, David E.)