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.[1] If object a is congruent with object b, we write a ≅ b and say, "a is congruent with b."

Manipulative 1 shows two congruent triangles. Click on the points on the sliders and the blue points on the triangles in the manipulative to change the figure. To place one triangle over the other, set horizontal, vertical and rotation to 0 and uncheck the Flip checkbox.

Properties of Congruent Figures

ManipulativeDescription
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. 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 8/6/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/21/mode/1up/search/congruent. Buy the book
  2. Williams, Cora Lenore. Syllabus of Plane Geometry. pp 13-14. www.archive.org. Standard Press. 1905. Last Accessed 8/6/2018. http://www.archive.org/stream/syllabusofplaneg00willrich#page/13/mode/1up/search/congruent. Buy the book

Cite this article as:

McAdams, David E. Congruent. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/congruent.html.

Image Credits

Revision History

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.)

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