What does the sign "≡" mean in mathematics?

Distinction from the equals sign (=): While the equals sign indicates that two expressions have the same value, the identity sign denotes that the expressions are fundamentally equivalent or interchangeable, regardless of the variable's value. Examples: An equation like 2x + 3 = 9 is only true for x = 3. However, an identity like (x + 1)² ≡ x² + 2x + 1 is true for any value you substitute for x.

Congruence in geometry is a = with a ~ over it.