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