1. a transformation of a geometric figure that preserves distances between all points, such as a rotation, reflection, or translation
Usage: mathematics; geometry
2. a correspondence between two metric spaces that preserves distances
Usage: mathematics; formal

Examples

• A reflection across a line is an example of an isometry because it preserves all distances.
• In geometry class, we learned that rotations and translations are both types of isometry.
• The isometry maps each point in the original figure to a corresponding point in the transformed figure.
• Mathematicians use isometry to study properties of shapes that remain unchanged under certain transformations.
• An isometry between two spaces means that the spaces have the same geometric structure.