symmetry
Exact likeness in shape about a given line (axis), point, or plane. A figure has symmetry if one half can be rotated and/or reflected onto the other. (Symmetry preserves length, angle, but not necessarily orientation.) In a wider sense, symmetry exists if a change in the system leaves the essential features of the system unchanged; for example, reversing the sign of electric charges does not change the electrical behaviour of an arrangement of charges.
Line symmetry
In the diagram, the letter A has one
line of symmetry, or mirror line, shown by the dotted line. This is the line of reflection:
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Rotational symmetry
The diagram shows that the shape may be rotated about O into three identical positions. It has rotational symmetry of order three:
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Transformation of shapes can also take place by translation, rotation, reflection, and enlargement.
