There are at least two meanings on the word congruent 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 ( divides ).

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., 1967.

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Weisstein, Eric W. "Congruent." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Congruent.html