Congruency of Triangles

 Congruent line segments Two line segments AB and CD are said to be congruent, if AB = CD. Congruent Angles Two angles ∠ABC and ∠DEF are said to be congruent, if they are equal. Congruent Triangles Two triangles are said to be congruent if their sides are congruent and their corresponding angles are congruent. The congruence relation is demonstrated by the symbol ΔABC≅ΔDEF Axioms of congruency SSS-axiom: If three sides of one triangle are equal to the three sides of the other triangle then the triangles are congruent. SAS-axiom: If two sides and included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle then the triangles are congruent. AAS-axiom: If two angles and one side of one triangle is correspondingly equal to the two angles and one side of the other triangle then the triangles are congruent. RHS-axiom: If the hypotenuse and one side of a right angled triangle is correspondingly equal to the hypotenuse and one side of the other right angled triangle then the triangles are congruent.