Definition:Congruence (Geometry)

This page is about Congruence in the context of Geometry. For other uses, see Congruence.

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