Similarity Transformations and Their Properties

Concept

Similarity Transformation

A combination of rigid motions and dilations is called a similarity transformation. The scale factor of a similarity transformation is the product of the scale factors of the dilations.

One triangle is mapped onto the other triangle using rigid motions and dilations

Move the slider to create a similarity transformation by combining rigid motions and dilations. Similar figures are created as the result of a similarity transformation.

Two similar figures of which one is mapped onto the other after applying rigid motions

Rule

Properties of Similarity Transformations

The following is a list of a few important properties of similarity transformations.

The image of a line segment is a line segment. The image is longer or shorter than the preimage in the ratio given by the scale factor.
Similarity transformations preserve angle measures.

Proof

These are properties of both rigid motions and dilations. Since similarity transformations are combinations of rigid motions and dilations, these are also properties of similarity transformations.

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Proof