Parallel
Pronunciation: /ˈpær əˌlɛl/ Explain
Click on the blue points and drag them to change the figure.
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.^{[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
Click on the blue points and drag them to change the figure.
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.^{[2]}

References
 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. http://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. 11/28/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/parallel.html.
Image Credits
Revision History
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.)