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AAA similarity theorem
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AAA similarity theorem

geometry
Also known as: angle-angle-angle similarity theorem
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Quick Summary

The AAA similarity theorem states that if two corresponding angles in two triangles are equal, then the two triangles are similar. This means they share the same shape and proportion, but not necessarily the same size.1

In Euclidean geometry, similarity can be proven using the side-angle-side (SAS) theorem, which states that if two corresponding sides and their included angles are equal in two triangles, then the triangles are congruent. The side-angle-side theorem can also be applied to similar triangles. If two corresponding sides from one triangle are in the same proportion to the corresponding sides in a second triangle, and the angles between these sides are equal, then the triangles are similar.2

Similar triangles are useful for determining measurements of objects that are difficult to measure directly, such as calculating the height of a tall tree using its shadow and the shadow of a known object.2

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2 Britannica Sources
  1. triangle
  2. side-angle-side theorem

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