Congruent

Pronunciation: /kənˈgru.ənt/ Explain

Click on the blue points and drag them to change the figure. Are two triangles still congruent if one is rotated relative to the other? Manipulative 1 - Congruent Triangles Created with GeoGebra.

Two geometric figures are congruent if they are the same shape and size, but may be flipped, moved, and/or rotated.[2] If object a is congruent with object b, we write a ≅ b and say, "a is congruent with b."

Properties of Congruent Figures

Manipulative	Description
	Two line segments are congruent if they have the same measure.
	Two angles are congruent if the measures of the angles are equal.
	Two shapes are congruent if each point on the shape corresponds with a point on the corresponding shape.
	The distance between two points on a figure and two corresponding points on a congruent figure is the same.

References

1. McAdams, David E.. All Math Words Dictionary, congruent. 2nd Classroom edition 20150108-4799968. pg 42. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 21. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 6/25/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/21/mode/1up/search/congruent. Buy the book
3. Williams, Cora Lenore. Syllabus of Plane Geometry. pp 13-14. www.archive.org. Standard Press. 1905. Last Accessed 6/25/2018. http://www.archive.org/stream/syllabusofplaneg00willrich#page/13/mode/1up/search/congruent. Buy the book

Cite this article as:

McAdams, David E. Congruent. 4/16/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/congruent.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

4/16/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/19/2010: Rewrote article. (McAdams, David E.)
12/2/2008: Updated definition. (McAdams, David E.)
3/25/2008: Changed More Information to match current standard. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)