Angle-Angle Similarity Theorem
if two angles in one triangle are equal to two angles in another triangle, then the triangles are similar.
The Angle-Angle Similarity Theorem, abbreviated as AA Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.
In other words, if two pairs of corresponding angles in two different triangles are equal in measure, then the triangles must be similar. This theorem is helpful in determining if two triangles are similar or not, even if their sides are not proportional.
This theorem is based on a crucial similarity property of triangles, which is that if two triangles are similar, then all of their corresponding angles are congruent, and their corresponding sides are proportional.
For example, if triangle ABC is similar to triangle DEF, and angle A is congruent to angle D, and angle B is congruent to angle E, then triangle ABC is similar to triangle DEF by AA Similarity Theorem.
The AA Similarity Theorem is used in geometry to prove more complex theorems and solve problems related to triangles and other polygons. It is an essential tool for understanding and working with similar triangles, which are important in many real-world applications.
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