Library/Geometry/Plane geometry/Triangles/Similar triangles/Criteria for similarity

Criteria for similarity

Overview
Important

Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. The criteria for similarity allow us to prove similarity using only part of this information.

Important properties

  • AA (Angle-Angle): If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

  • SSS (Side-Side-Side): If the three sides of one triangle are proportional to the three sides of another triangle, the triangles are similar.

  • SAS (Side-Angle-Side): If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

  • If two triangles are similar, then the ratios of their corresponding sides are equal, and their corresponding angles are equal.