Pronunciation: /ɪnˈvɛər i ənt/ Explain

Properties of a mathematical object undergoing a transformation that are unchanged by the transformation are called invariant. Manipulative 1 shows a dilation of a triangle. Properties of a triangle that are invariant under dilation are the measures of the angles, and the ratios between the measures of the sides. Properties of the triangle that are not invariant are the lengths of the sides and the area of the triangle.

Click on points and drag them to change the figure.

Which of the following never change for dilation: Angle measure, length of side, ratio of sides, are of the triangle?
Manipulative 1 - Invariant Created with GeoGebra.


  1. Glenn, Oliver E.. A Treatise on the Theory of Invariants. Ginn and Company. 1915. Last Accessed 8/6/2018. Buy the book
  2. Lin I-hsiung. Geometric Linear Algebra. vol 2 pg 194-205. World Scientific Publishing Company. May 6, 2008. Buy the book
  3. A. B. Kharazishvili. Transformation Groups and Invariant Measures: Set-Theoretical Aspects. World Scientific Publishing Company. September 1998. Buy the book

Cite this article as:

McAdams, David E. Invariant. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Image Credits

Revision History

8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/2/2010: Added "References", clarified wording. (McAdams, David E.)
9/16/2008: Initial Version. (McAdams, David E.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License