Angle and Angle Axiom (ASA) has the congruence of two triangles, which have two angles and their sides correspond to each other.

Angular axiom (SAS) has the consistency of two sides and two triangles with equal included angles.

Reasoning (AAS) has two angles, and the opposite side of one angle corresponds to the coincidence of two triangles.

The edge axiom (SSS) has two triangles and three corresponding equilateral sides.

The axiom of hypotenuse and right angle (HL) has the coincidence of hypotenuse and right angle corresponding to two right triangle.