# Congruence

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**Congruence** may refer to:

## Mathematics

- [Congruence (geometry)](/source/Congruence_(geometry)), being the same size and shape
- Congruence or [congruence relation](/source/Congruence_relation), in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
- In [modular arithmetic](/source/Modular_arithmetic), having the same remainder when divided by a specified integer - [Ramanujan's congruences](/source/Ramanujan's_congruences), congruences for the partition function, *p*(*n*), first discovered by Ramanujan in 1919 - [Congruence subgroup](/source/Congruence_subgroup), a subgroup defined by congruence conditions on the entries of a matrix group with integer entries - [Congruence of squares](/source/Congruence_of_squares), in number theory, a congruence commonly used in integer factorization algorithms
- [Matrix congruence](/source/Matrix_congruence), an equivalence relation between two matrices
- [Congruence (manifolds)](/source/Congruence_(manifolds)), in the theory of smooth manifolds, the set of integral curves defined by a nonvanishing vector field defined on the manifold
- [Congruence (general relativity)](/source/Congruence_(general_relativity)), in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of spacetime or a bundle of world lines
- [Zeller's congruence](/source/Zeller's_congruence), an algorithm to calculate the day of the week for any date
- [Scissors congruence](/source/Scissors_congruence), related to Hilbert's third problem

## Mineralogy and chemistry

In mineralogy and chemistry, the term congruent (or incongruent) may refer to:

- [Congruent dissolution](/source/Solubility#Incongruent_dissolution): substances dissolve congruently when the composition of the solid and the dissolved solute stoichiometrically match
- [Congruent melting](/source/Congruent_melting) occurs during melting of a compound when the composition of the liquid that forms is the same as the composition of the solid
- [Incongruent transition](/source/Incongruent_transition), in chemistry, is a mass transition between two phases which involves a change in chemical composition

## Psychology

- In Carl Rogers' personality theory, the compliance between ideal self and actual self; see [Carl Rogers § Incongruity](/source/Carl_Rogers#Incongruity)
- [Mood congruence](/source/Mood_congruence) between feeling or emotion (in psychiatry and psychology)
- Incongruity [theory of humor](/source/Theory_of_humor)

## See also

- [Congruence bias](/source/Congruence_bias), a type of cognitive bias, similar to confirmation bias
- [Congruence principle (disambiguation)](/source/Congruence_principle_(disambiguation))
- [Hatch mark](/source/Hatch_mark), geometric notation for congruent line segments
- [≅](/source/%E2%89%85)
- [≡ (disambiguation)](/source/%E2%89%A1_(disambiguation))
- [≃](/source/%E2%89%83)

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Adapted from the Wikipedia article [Congruence](https://en.wikipedia.org/wiki/Congruence) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Congruence?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.