Concurrent
Pronunciation: /kənˈkɜr ənt/ ?
 Manipulative 1: Points of concurrency. 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
 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
 Manipulative 4: Concurrent objects. 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
 concurrent. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 20110108). http://wordnetweb.princeton.edu/perl/webwn?s=concurrent&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
 Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 7. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 20100102). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/7/mode/1up/search/concurrent.
 Hart, C. A.; Feldman, Daniel D.. Plane Geometry, pg 72. American Book Company, 1911. (Accessed: 20100118). http://www.archive.org/stream/geometryplane00hartrich#page/72/mode/1up/search/concurrent.
Cite this article as:
Concurrent. 20100118. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/concurrent.html.
Translations
Image Credits
Revision History
20100118: Added "References" and removed section on concentric circles. (
McAdams, David.)
20091221: Added reference to Euclid's Elements; Expanded table of angle classes. (
McAdams, David.)
20081119: Expanded from just lines to geometric figures (
McAdams, David.)
20080709: Added More Information (
McAdams, David.)
20080425: Initial version (
McAdams, David.)