Definition: The AA criterion states that if two angles of one triangle are congruent to two angles of another, then the two triangles are similar.
Why are two angles enough?
The angles of a triangle always sum to 180 degrees. If two pairs match, the third pair must match too. Triangles with all angles equal have the same shape, with corresponding sides in proportion.
How is it used?
To prove similarity, then write proportions between corresponding sides to find unknown lengths. A typical setup uses a pair of vertical angles, a shared angle, or parallel lines that create equal angles.
Example. A 1.8 m person casts a shadow 2.4 m long. At the same moment, a tree casts a shadow 14 m long. The sun makes the same angle with the ground for both, and each has a right angle, so the triangles are similar by AA. Then h / 14 = 1.8 / 2.4, so h = 14(0.75) = 10.5 m.
What errors occur?
Matching sides in the wrong order when writing the proportion. List the vertices in corresponding order first. Another error is to say the triangles are congruent; AA gives the same shape, not the same size. Equal sides are needed for congruence.