Congruent

Pronunciation: /kənˈgru ənt/ ?

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Manipulative 1: Congruent Triangles.

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
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Two line segments are congruent if they have the same measure.
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) 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. congruent. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=congruent&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pg 21. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-30). http://www.archive.org/stream/elementsofconstr00noetrich#page/21/mode/1up/search/congruent.
  3. Williams, Cora L.. Syllabus of Plane Geometry, pp 13-14. Standard Press, 1905. (Accessed: 2010-01-19). http://www.archive.org/stream/syllabusofplaneg00willrich#page/13/mode/1up/search/congruent.

Cite this article as:


Congruent. 2010-01-19. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/congruent.html.

Translations

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Revision History


2010-01-19: Rewrote article (McAdams, David.)
2008-12-02: Updated definition (McAdams, David.)
2008-03-25: Changed More Information to match current standard (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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