Students learn that rigid motions can be used as a tool to show congruence. Topic C merges the concepts of specificity of definitions, constructions, and proof to formalize rigid motions studied in 8th grade. In Topic B, students formalize understanding developed in middle school geometry of angles around a point, vertical angles, complementary angles, and supplementary angles through organizing statements and reasons for why relationships to construct a viable argument. Students are introduced to the concept of a construction, and use the properties of circles to construct basic geometric figures. Unit 1 begins with students identifying important components to define- emphasizing precision of language and notation as well as appropriate use of tools to represent geometric figures. This unit lays the groundwork for constructing mathematical arguments through proof and use of precise mathematical vocabulary to express relationships. These rigid motion transformations are introduced through points and line segments in this unit, and provide the foundation for rigid motion and congruence of two-dimensional figures in Unit 2. Transformations that preserve angle measure and distance are verified through constructions and practiced on and off the coordinate plane. In Unit 1, Constructions, Proof and Rigid Motion, students are introduced to the concept that figures can be created by just using a compass and straightedge using the properties of circles, and by doing so, properties of these figures are revealed.

Rigid motion in mathematics