AA Similarity

Pronunciation: /eɪ eɪ ˌsɪm ə'lær ɪ ti/ Explain

In Euclidean geometry, two triangles are known to be similar if two corresponding angles are congruent.[1] 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.

In manipulative 1, angles A and A' are congruent and angles B and B' are congruent. Click on the blue points in manipulative 1 and drag them to change the figure.

Manipulative 1: Similar triangles by AA similarity

References

  1. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 83. D. Van Nostrand Company, 1908. 1/4/2010. http://www.archive.org/stream/mathengineer00kellrich#page/83/mode/1up/search/Similarity.

Cite this article as:


AA Similarity. 6/12/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/aasimilarity.html.

Image Credits

Revision History


5/8/2018: Updated Geogebra app. (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.)

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