Lesson objective: Fluently understand that an image resulting from a series of different transformations (dilations, rotations, reflections, or translations) is similar to the original shape because the corresponding lengths have a common scale factor and the corresponding angles are congruent.

Students bring prior knowledge of proportionality from 7.RP.A.2. This prior knowledge is extended to images resulting from a series of transformations. A conceptual challenge students may encounter is performing more than one transformation on a preimage.

The concept is developed through work with a grid or coordinate plane, which allows students to identify lengths and transformations using ordered pairs or the squares on the grid.

This work helps students deepen their understanding of equivalence because corresponding angles are congruent while the scale factor describes the relationship of the side lengths when a series of transformations are performed on a preimage.

Students engage in Mathematical Practice 6 (attend to precision) as they identify relationships in similar shapes when they apply scale factors to coordinates. Students should notice that the angles remain the same while the sides may decrease, increase, or remain the same.

**Key vocabulary:**

- dilation
- enlargement
- reduction
- rotation
- scale factor
- transformation
- translation

**Special materials needed:**

- graph or grid paper
- highlighters or colored pencils to assist students in identifying the various images