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If P and Q are points in the plane, |PQ| denotes the distance between P and Q. An isometry is a transformation of the plane that preserves the distance between points: it is a transformation with the property that, if P and Q are mapped to P′ and Q′, then |PQ′| =|PQ|. Examples of isometries are translations, rotations and reflections. It can be shown that all the isometries of the plane can be obtained from translations, rotations and reflections, by composition. Two figures are congruent if there is an isometry that maps one onto the other.

Subjects: Mathematics.

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