Congruent Symbol in LaTeX

For congruent triangles or isomorphic objects write \cong (≅): \triangle ABC \cong \triangle DEF. For modular congruence write \equiv (≡) with \pmod: a \equiv b \pmod{n}. The negations are \ncong (amssymb) and \not\equiv.

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Congruence symbols

A \cong B
$A ≅ B$
≅: congruent (geometry) or isomorphic (algebra).
A \ncong B
$A ≇ B$
≇: not congruent (amssymb).
a \equiv b \pmod{n}
$a \equiv b (\mod n)$
≡ with the modulus in parentheses.
a \not\equiv b \pmod{n}
$a ≢ b (\mod n)$
Not congruent modulo n.
f \equiv 0
$f \equiv 0$
≡ also means "identically equal" or "defined as".
a \sim b
$a \sim b$
∼: similar or equivalent, a weaker relation.

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Congruent (≅, ≡) examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Congruent triangles
$△ A B C ≅ △ D E F$
LaTeX
```
\triangle ABC \cong \triangle DEF
```
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Isomorphic groups

Z / 6 Z ≅ Z / 2 Z \times Z / 3 Z

LaTeX

\mathbb{Z}/6\mathbb{Z} \cong \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/3\mathbb{Z}

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Modular congruence
$17 \equiv 2 (\mod 5)$
LaTeX
```
17 \equiv 2 \pmod{5}
```
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Fermat's little theorem
$a^{p - 1} \equiv 1 (\mod p)$
LaTeX
```
a^{p-1} \equiv 1 \pmod{p}
```
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Not congruent
$4 ≢ 1 (\mod 2)$
LaTeX
```
4 \not\equiv 1 \pmod{2}
```
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Identically zero
$f (x) \equiv 0 on [0, 1]$
LaTeX
```
f(x) \equiv 0 \quad \text{on } [0, 1]
```
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Which symbol means what

≅ (\cong) is used for congruent figures in geometry and for isomorphisms in algebra and topology. ≡ (\equiv) is used for congruence modulo n, for "identically equal" and in some texts for definitions. ∼ (\sim) is for similar triangles or a general equivalence relation.

Writing the modulus

\pmod{n} adds space and parentheses: "a ≡ b (mod n)". \bmod is the binary operator in "a mod n", and \mod{n} and \pod{n} are variants with and without the word or the parentheses. See the modulo page for all four.

Common mistakes

Typed "mod" is set in italic letters as a product m·o·d.
Instead of
```
a \equiv b (mod n)
```
Write
```
a \equiv b \pmod{n}
```
\ncong comes from amssymb.
Instead of
```
A \ncong B  (no amssymb)
```
Write
```
\usepackage{amssymb}
```
Most curricula use ≅ for congruent figures; ≡ is the modular or identity symbol.
Instead of
```
\triangle ABC \equiv \triangle DEF
```
Write
```
\triangle ABC \cong \triangle DEF
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\cong, \equiv, \pmod need nothing; \ncong needs amssymb.
MathJax and KaTeX
MathJax and KaTeX support \cong, \ncong, \equiv, \not\equiv and \pmod.
Microsoft Word
In a Word equation \cong then Space gives ≅ and \equiv gives ≡.

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Congruent (≅, ≡) in LaTeX: questions

What is the LaTeX command for the congruent symbol?: \cong for ≅. For modular congruence use \equiv (≡).
How do I write a ≡ b mod n?: a \equiv b \pmod{n}.
How do I write "not congruent"?: \ncong (with amssymb) or \not\equiv.

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Congruent Symbol in LaTeX

Congruence symbols

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Congruent (≅, ≡) examples

Congruent triangles

Isomorphic groups

Modular congruence

Fermat's little theorem

Not congruent

Identically zero