Isometry
A translation that preserves length,angle,measure, and area- image congruent to pre image
Isometry is a type of transformation in geometry that preserves the size, shape, and distance of objects. An isometry is a mapping between two geometric objects that maintains their geometric properties such as orientation, shape, and size. In other words, it is a transformation that preserves the underlying structure of the objects being transformed.
Isometries can be classified into two categories – direct isometries and indirect isometries. Direct isometries maintain the handedness of the objects, while indirect isometries change the handedness of the objects. Examples of direct isometries include translations, rotations, and reflections, while glide reflections are examples of indirect isometries.
Isometries play an important role in various areas of mathematics including geometry, topology, and group theory. They are used to describe the symmetries of objects and to study the properties of geometric objects under transformations. Additionally, isometries have practical applications in fields such as computer graphics and engineering, where they are used to model and analyze physical systems.
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