Angle-angle-side (AAS) congruence states that if any two consecutive angles of a triangle are equal in measure to two consecutive angles of another triangle and a pair of corresponding not included sides to these angles is congruent; then the two triangles are congruent; that is, they have exactly the same shape and size.

Angle-side-angle (ASA) congruence states that if any two angles of a triangle are equal in measure to two angles of another triangle and the side in between each pair of angles have the same length, then the two triangles are congruent; that is, they have exactly the same shape and size.

Included angle
The angle made by two intersecting sides of a polygon.

Included side
The side between two consecutive angles in a polygon.

Side-angle-side (SAS) congruence states that if any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size.

The side-side-side (SSS) congruence states that if the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent.