Library/Geometry/Plane geometry/Triangles/Equal triangles. Criteria for equality

Equal triangles. Criteria for equality

Overview
Important

Two triangles are congruent if all their corresponding sides and angles are equal. There are several criteria that allow us to prove two triangles are congruent without checking all sides and angles:

Important properties

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

  • SAS (Side-Angle-Side): If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, the triangles are congruent.

  • ASA (Angle-Side-Angle): If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, the triangles are congruent.

  • AAS (Angle-Angle-Side): If two angles and a non-included side in one triangle are equal to two angles and the corresponding non-included side in another triangle, the triangles are congruent.

  • RHS (Right angle-Hypotenuse-Side): For right-angled triangles, if the hypotenuse and one other side are equal, the triangles are congruent.

Deeper topics