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. 