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Reference

# 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.
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.
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.