The three properties of congruence are the reflexive property, the symmetric property and the transitive property.

Any geometric figure is congruent to itself. For example, the segment $\overline{AB}$ is always congruent with itself. $\overline{AB}\ \cong\overline{AB}$

If a given geometric object, $A,$ is congruent with another geometric object, $B,$ then $B$ is also congruent with $A.$ For example, if triangle $A$ is congruent with triangle $B,$ then $B$ is also congruent with $A.$ $\triangle A \cong \triangle B \quad\text{then} \quad \triangle B \cong \triangle A$

If geometric objects $A$ and $B$ are congruent and $B$ is also congruent with $C,$ then $A$ is congruent with $C.$ $\text{If }\angle A\cong\angle B\ \text{and}\ \angle B\cong\angle C,\ \text{then}\ \angle A\cong\angle C$ In this example, angles $A$ and $C$ are congruent because $\angle A$ is congruent with $\angle B$ and $\angle B$ is congruent with $\angle C.$