Similar Triangles

AA (Angle-Angle) Similarity

If two angles of one Triangle are congruent to two angles of another Triangle, the triangles are similar.

SSS (Side-Side-Side) Similarity

If all three pairs of corresponding sides are proportional, the triangles are similar.

SAS (Side-Angle-Side) Similarity

If two pairs of corresponding sides are proportional and the included angles are congruent, the triangles are similar.

Why AA Works

If two angles are congruent, the third must also be congruent (since angles sum to 180°). Once all angles match, the sides are automatically proportional.

Example

Given two triangles with angles 40°, 60°, 80° and 40°, 60°, 80°: the triangles are similar by AA (two pairs of angles match).