Geometric transformation that preserves the measures of the figures (lengths, angles) or distances.

The word

*isometry*also refers to the property of that which is isometric. We can determine the isometry of two figures by examining the measures of their sides and their corresponding angles.### Properties

- A
**direct isometry**preserves the orientation of the plane.

Translations and rotations are direct isometries.

- An
**opposite isometry**is an isometry that inverts the orientation of the plane.

An opposite isometry is also called a flip.

Orthogonal symmetries, also called reflections, and glide reflection symmetries are opposite isometries.

- The expression
**negative isometry**is a synonym for opposite isometry or flip. - The expression
**positive isometry**is a synonym for direct isometry.