The four standard congruence tests for triangles

Two triangles are congruent if:

SSS: the three sides of one triangle are respectively equal to the three sides of the other triangle, or

SAS: two sides and the included angle of one triangle are respectively equal to two sides and the included angle of the other triangle,

AAS: two angles and one side of one triangle are respectively equal to two angles and the matching side of the other triangle,

RHS: the hypotenuse and one side of one right-angled triangle are respectively equal to the hypotenuse and one side of the other right-angled triangle.

Each congruence test will be justified by finding out what is a minimal amount of information − in terms of side lengths and angle sizes − needed to construct a triangle that is unique up to congruence.