Lesson objective: Understand that shapes with the same name are not necessarily similar. To be similar, the shapes must have the same scale factor or ratio when comparing dimensions.

Students bring prior knowledge of proportionality from 7.RP.A.2. This prior knowledge is extended to dilations as students apply a scale factor to ordered pairs. A conceptual challenge students may encounter is the scale factor or ratio describing the relationships of the dimensions must be equivalent for the shapes to be similar.

The concept is developed through work with coordinate planes, which allow students to identify the coordinates of the preimage then apply the scale factor to the coordinates or determines dimensions using 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.

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
- scale factor

**Special materials needed:**