# Properties of Congruence

The following are the properties of congruence . Some textbooks list just a few of them, others list them all. These are analogous to the properties of equality for real numbers. Here we show congruences of angles , but the properties apply just as well for congruent segments , triangles , or any other geometric object.

 PROPERTIES OF CONGRUENCE Reflexive Property For all angles $A$ , $\angle A\cong \angle A$ . An angle is congruent to itself. These three properties define an equivalence relation Symmetric Property For any angles $A\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}B$ , if $\angle A\cong \angle B$ , then $\angle B\cong \angle A$ . Order of congruence does not matter. Transitive Property For any angles $A,B,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}C$ , if $\angle A\cong \angle B$ and $\angle B\cong \angle C$ , then $\angle A\cong \angle C$ . If two angles are both congruent to a third angle, then the first two angles are also congruent.