What Do Isometries Preserve?

What Do Isometries Preserve? An isometry of the plane is a linear transformation which preserves length. Isometries include rotation, translation, reflection, glides, and the identity map. Two geometric figures related by an isometry are said to be geometrically congruent (Coxeter and Greitzer 1967, p. 80). Do isometries preserve angles? In Euclidean geometry, every distance-preserving map