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.[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

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.[3]

References

1. McAdams, David E.. All Math Words Dictionary, parallel. 2nd Classroom edition 20150108-4799968. pg 134. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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
3. 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
4. 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.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.)