# Definitions Let $(X_{1},d_{1}),(X_{2},d_{2})$ be [[Metrics|metric spaces]]. An isometry is a [[Distance-preserving maps between metric spaces|distance preserving map]] $f:X_{1}\to X_{2}$ that is surjective and hence bijective (since distance-preserving maps are automatically injectve). If an isometry exists between them, $(X_{1},d_{1})$ and $(X_{2},d_{2})$ are said to be *isometric*. > [!Example] Example > [[General form of Plane Isometries]]. # Properties(s) # Application(s) **More examples**: # Bibliography