Two triangles are said to be congruent when all their corresponding sides and corresponding angles are equal in measure. The congruence of two triangles, having only some angles' and sides' measures of both, can be proved by the following congruence postulates:
SSS : Side  Side  Side

SSS axiom of Congruence 
When all three sides of two triangles are equal, they are said to be congruent
SAS : Side  Angle  Side

SAS axiom of Congruence 
When two sides, and one included angle of two triangles are equal in measure, they are said to be congruent
ASA : Angle  Side  Angle

ASA axiom of Congruence 
When two angles, and one included side of two triangles are equal in measure, they are said to be congruent.
AAS : Angle  Angle  Side

AAS axiom of Congruence 
When two angles and one side (not included) of two triangles are equal in measure, they are said to be congruent.
HL or HypS : Hypotenuse leg

HL or HypS axiom of Congruence 
When the hypotenuse (longest side of a right angled triangle) and one other side of two right triangles are equal, they are said to be congruent.
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