Concurrent

Pronunciation: /kənˈkɜr ənt/ Explain
Click on the blue points and drag them to change the figure.

The red points are the points of concurrency.
Manipulative 1 - Concurrent Created with GeoGebra.

Two or more geometric figures are concurrent at a point if they share that point[1][2]. The shared point is called the point of concurrency. A point of concurrency the same thing as an intersection.

Manipulative 1 shows several figures. Points where the figures are concurrent are red. Click on the blue points in manipulative 1 and drag them to change the figure. If the red points disappear, the figures are not concurrent.

Concurrent lines

Click on the points and drag them to change the figure.

What can you say about two lines that are not concurrent.
Manipulative 2 - Concurrent Lines Created with GeoGebra.
Two straight lines have either 0 or 1 concurrencies. If two lines have 0 concurrencies, the lines are parallel. If they have 1 concurrency, the lines are not parallel. Click on the blue points in manipulative 2 and drag them to change the figure. Note that the two lines might intersect outside of the view window of manipulative 2.

Discovery

Click on the blue points and drag them to change the figure.

The red points are the points of concurrency.
Manipulative 3 - Concurrent Obects Created with GeoGebra.

Use manipulative 4 to find the answers to the following questions.

  • What is the least number of concurrencies of an arbitrary circle and an arbitrary square?
  • What is the greatest number of concurrencies of an arbitrary circle and an arbitrary square?

References

  1. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 7. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 8/6/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/concurrent. Buy the book
  2. Hart, C. A.; Feldman, Daniel D.. Plane Geometry. pg 72. www.archive.org. American Book Company. 1911. Last Accessed 8/6/2018. http://www.archive.org/stream/geometryplane00hartrich#page/72/mode/1up/search/concurrent. Buy the book

Cite this article as:

McAdams, David E. Concurrent. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/concurrent.html.

Image Credits

Revision History

8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/18/2010: Added "References" and removed section on concentric circles. (McAdams, David E.)
12/21/2009: Added reference to Euclid's Elements; Expanded table of angle classes. (McAdams, David E.)
11/19/2008: Expanded from just lines to geometric figures. (McAdams, David E.)
7/9/2008: Added More Information. (McAdams, David E.)
4/25/2008: Initial version. (McAdams, David E.)

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