Angle-Angle Similarity

Pronunciation: /ˈæŋ.gəl ˈæŋ.gəl ˌsɪm.ə'lær.ɪ.ti/ Explain
Abbreviation: AA Similarity

In Euclidean geometry, two triangles are known to be similar if two corresponding angles are congruent.^[2] Two angles are congruent if they have the same measure. This is called AA similarity. AA stands for angle, angle.

If ΔA is similar to ΔB, write "ΔA ∼ ΔB" and say, "Triangle A is similar to triangle B."

In Euclidean geometry the sum of the angles of a triangle is always 180° = 2π rad. This means that if two corresponding angles are congruent between two triangles, then the third angle must also be congruent. This is sometimes called AAA similarity for angle-angle-angle similarity. However, since AAA similarity is exactly the same thing as AA similarity, this term is rarely used.

Click on the blue points and drag them to change the figure. Angles A and A' are congruent and angles B and B' are congruent. When you change the figure, what does not change?

Manipulative 1 - Angle-Angle Similarity (AA Similarity) Created with GeoGebra.

References

1. McAdams, David E.. All Math Words Dictionary, AA similarity. 2nd Classroom edition 20150108-4799968. pg 8. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 83. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 6/12/2018. http://www.archive.org/stream/mathengineer00kellrich#page/83/mode/1up/search/Similarity. Buy the book

More Information

• Triangle similarity postulates/criteria. www.khanacademy.org. Kahn Academy. 6/19/2018. https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similarity-postulates.
• Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.

Cite this article as:

McAdams, David E. Angle-Angle Similarity. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/aasimilarity.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

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/4/2010: Added "References". (McAdams, David E.)
9/16/2008: Change manipulative from Geometer's Sketchpad to Geogebra. (McAdams, David E.)
9/3/2007: Added paragraph on AAA similarity. (McAdams, David E.)
8/25/2007: Replaced graphic in figure 1 with manipulative. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)