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Angle-Angle (AA) Similarity Theorem
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The Angle-Angle (AA) Similarity Theorem states that if two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar.
Explanation:
Since the angles match, the triangles have the same shape, even if they are different sizes. The third angle will also be congruent, and the corresponding side lengths will be proportional.
Example:
Suppose in △ABC and △DEF:
∠A ≅ ∠D
∠B ≅ ∠E
Then, by the AA Similarity Theorem, △ABC ~ △DEF. This means:
∠C ≅ ∠F
Corresponding side lengths are proportional
For example:
AB/DE = BC/EF = AC/DF
The triangles are similar, not necessarily congruent, because they may be different sizes.
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