Movement of a shape can involve flexing - for example, a square frame being flexed into a rhombus. Rigid motion excludes such motion: the shape of the moving object does not change.
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dilation (APEX)
Stretch
Rigid motion
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
There are different kinds of geometry including elementary geometry, Euclidean geometry, and Elliptic Geometry.