The purpose of this section is for students to describe translations, rotations, and reflections using precise language as well as accurately draw these transformations with and without a grid and coordinate points. Students shift from informal descriptions to precise mathematical language that identifies specific features of each transformation throughout the section. Throughout this section, student language is recorded as a...

The purpose of this section is for students to connect their understanding of rigid transformations with congruence of figures. While finding a difference between features of two figures is sufficient to show the figures are not congruent, comparing features may not be enough to show that two shapes are congruent. Identifying a rigid transformation that takes one shape to the...

The purpose of this section is for students to apply their understanding of rigid transformations to figures involving parallel lines and transversals. First, students use 180-degree rotations about a point to show that parallel lines cut by a transversal have congruent alternate interior angles.
Then students connect their prior understanding about straight angles with angles in a triangle as they...

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions. All lessons in this section are optional.

The purpose of this section is for students to explore important properties of rigid transformations and use these properties to make arguments about the features of particular figures and their transformations. First, students observe that for a figure and its image under a translation, rotation, or reflection, corresponding sides are the same length and corresponding angles are the same measure....

During these lessons students think about what conditions are needed to determine a unique figure, in preparation for future work with congruence in grade 8 and high school. These lessons continue the language used in grade 6: Two polygons are identical if they match up exactly when placed one on top of the other.

Students first experiment with creating polygons...