# 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[2][3]. The shared point is called the point of concurrency. A point of concurrency the same thing as an intersection.

### 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. Note that the two lines in manipulative 2 might intersect outside of the view window.

### 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 3 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. McAdams, David E.. All Math Words Dictionary, concurrent. 2nd Classroom edition 20150108-4799968. pg 41. 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 7. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 6/25/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/concurrent. Buy the book
3. Hart, C. A.; Feldman, Daniel D.. Plane Geometry. pg 72. www.archive.org. American Book Company. 1911. Last Accessed 6/25/2018. http://www.archive.org/stream/geometryplane00hartrich#page/72/mode/1up/search/concurrent. Buy the book

McAdams, David E. Concurrent. 3/9/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/concurrent.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)