The word congruent has several meanings in mathematics.
Two geometric figures are said to be congruent if one can be transformed into the other by an isometry (Coxeter and Greitzer 1967, p. 80).
This relationship, called geometric congruence,
is written 
.
(Unfortunately, the symbol 
is also used to denote an isomorphism.)
A number 
is said to be congruent to 
modulo 
if 
. Equivalently, 
divides 
.
In linear algebra, two square matrices 
and 
are congruent matrices if 
for some nonsingular
matrix 
.
