The focus of this lesson is on quadrilaterals and ways to decide whether or not they are similar. Since the transformations we have studied (translations, rotations, reflections, dilations) do not change angle measures, similar polygons will have congruent corresponding angles. Also, since dilations change all side lengths by the same scale factor, similar polygons will have proportional corresponding side lengths. While these two key ideas can determine whether two polygons are not similar, using them to determine that polygons are similar will not be formally proven until high school. In grade 8, similar figures are identified using transformations.

Students begin the lesson by considering whether similarity and congruence are mutually exclusive. This prepares students to use what they know about side lengths and angle measures to determine if two figures are similar or not and explain their reasoning (MP3). In the last activity, students are given a card with a figure and must find another student in the room with a similar (but not congruent) figure, again explaining why their two figures are similar (MP3).