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Symmetry comes from a Greek word meaning 'to measure together' and is widely used in the study of geometry. Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide.
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other. A geometric object has symmetry if there is an operation or transformation (technically, an isometry or affine map) that maps the figure/object onto itself; i.e., it is said that the object has an invariance under the transform.