Similarity transformations
Overview
Important
A similarity transformation is a transformation of the plane that changes figures so that their shapes remain the same, but their sizes may change. It is any combination of basic transformations: translation, rotation, reflection, and dilation (scaling from a point). Under a similarity transformation, all distances are multiplied by the same positive scale factor, and all angles are preserved.
Important properties
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Similarity transformations map lines to lines and preserve angles.
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The ratio of lengths between any two corresponding segments is constant (the scale factor).
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Composing two similarity transformations results in another similarity transformation.
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Congruence transformations (isometries) are special cases of similarity transformations with scale factor 1.