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.

In this section, students examine the rigid transformations that take some shapes to themselves, otherwise known as symmetries. Then students continue describing sequences of rigid transformations that take one figure to another, congruent, figure.

To prepare students for future congruence proofs, students start to come up with a systematic, point-by-point sequence of transformations that will work to take any pair...

In this section students create conjectures about angle relationships and prove them using what they know about rigid transformations.

The primary work is on proof-writing skills. In order to focus on justification, many proofs are for ideas students were first introduced to in previous grades, such as supplementary, complementary, vertical, and adjacent angles. Students also prove the Triangle Angle Sum...

In this section, students study transformations both on and off of grids. Providing the structure of a grid allows students to make connections with their learning in previous courses. Then students learn precise definitions for the rigid motions, translations, reflections, and rotations that apply off the grid.

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Students recall that the figures are called congruent if...

In this section, students use rigid compasses and straightedges to develop a catalog of construction techniques that they can use to construct a variety of figures.

Students begin by following instructions and making observations about figures. Then they write their own instructions and identify ways to attend to precision in their communication. Multiple lessons include perpendicular lines. This key building...