Congruent in LaTeX (\cong)

Where it is used

Tilde over an equals sign denoting isomorphism of structures or congruence of geometric figures.

Algebraists write G \cong H for isomorphic groups and V \cong V^{**} for finite-dimensional spaces, while geometry uses \triangle ABC \cong \triangle DEF for congruent triangles. Some physics and engineering texts use it to mean approximately equal, but \approx is clearer for that. It differs from \simeq (a single bar, used for homotopy equivalence or asymptotic equality) and from \equiv (three bars). To label the map, place it over the symbol with \overset{\phi}{\cong} or use an arrow like \xrightarrow{\sim}.

Also listed under: Geometry, Topology & Abstract Math

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amssymb}
\begin{document}
Congruent: $\cong$

\[ \mathbb{Z}/6\mathbb{Z} \cong \mathbb{Z}/2 \times \mathbb{Z}/3 \]
\end{document}

Related symbols

• Subset\subset
• Similar To\sim
• Subset or Equal\subseteq
• Proportional To\propto
• Proper Subset\subsetneq
• Equivalent\equiv

Frequently asked questions

How do I write Congruent in LaTeX?

Type \cong in math mode, for example $\mathbb{Z}/6\mathbb{Z} \cong \mathbb{Z}/2 \times \mathbb{Z}/3$. It works in plain LaTeX without loading any package.

Which package do I need for \cong?

None. \cong is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \cong in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\cong$ in running text. If you only need the glyph in text, paste the Unicode character ≅ instead (with XeLaTeX or LuaLaTeX and a font that has it).