In this lesson, students construct and compare several examples of dilated figures. They then measure and compare corresponding lengths in the dilated and original figures. This leads to a conjecture that all distances after the dilation are multiplied by the same ratio given by the scale factor.

Students must be precise in their understanding of the definition of dilation to correctly draw and understand the scaled figures (MP6).

Note on language: In previous courses, students may have learned that a ratio is an association between two or more quantities. However, in more advanced work, such as this course, ratio is commonly used as a synonym for quotient (which some refer to as the value of the ratio). This expanded use of the word ratio comes into play in this lesson when students are asked to write fractions representing ratios and notice connections between the fraction and the scale factor. In later lessons, the terms “scale factor” and “ratio of side lengths” are used interchangeably, and the term “ratio” is used to mean “the quotient."