Summary :
SSS Congruence of two triangles:
Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other.
SAS Congruence of two triangles:
Under a given correspondence, two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle.
ASA Congruence of two triangles:
Under a given correspondence, two triangle are congruent if two angles are and the sides included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.
RHS Congruence of two –right angled triangles:
Under a given correspondence, two right – angled triangles are congruent if the hypotenuse and a leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle.
There are no such thing as AAA Congruence of two triangles:
Two triangles, with equal corresponding angles need not to be congruent. In such a correspondence, one of them can be enlarged copy of the other. (They would be congruent only if they are exact copies of one another).