The set of all transformations that can be built out of successive translations, rotations, and reflections is called the group of isometries. It can also be defined as the group that preserves dot pr...The set of all transformations that can be built out of successive translations, rotations, and reflections is called the group of isometries. It can also be defined as the group that preserves dot products, or the group that preserves congruence of triangles.
