# Definition:Congruence (Geometry)

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## Definition

In the field of Euclidean geometry, two geometric figures are **congruent** if they are, informally speaking, both "the same size and shape".

That is, one figure can be overlaid on the other figure with a series of rotations, translations, and reflections.

Specifically:

- all corresponding angles of the
**congruent**figures must have the same measurement - all corresponding sides of the
**congruent**figures must be be the same length.

## Also see

- Triangle Side-Angle-Side Equality
- Triangle Side-Side-Side Equality
- Triangle Angle-Angle-Side Equality
- Triangle Angle-Side-Angle Equality

## Historical Note

The symbol introduced by Gottfried Wilhelm von Leibniz to denote geometric congruence was $\simeq$.

This is still in use and can still be seen, but is not universal.

Also in current use is $\cong$.

## Sources

- 2018: John M. Lee:
*Introduction to Riemannian Manifolds*(2nd ed.) ... (next): $\S 1$: What Is Curvature? The Euclidean Plane