Transformations/Rigid Motions

Description

Topic C, Transformations, builds on students’ intuitive understanding developed in Grade 8. With the help of manipulatives, students observed how reflections, translations, and rotations behave individually and in sequence (8.G.1, 8.G.2). In Grade 10, this experience is formalized by clear definitions (G.CO.4) and more in-depth exploration (G.CO.3, G.CO.5).

The concrete establishment of rigid motions also allows proofs of facts formerly accepted to be true (G.CO.9). Similarly, students’ Grade 8 concept of congruence transitions from a hands-on understanding (8.G.2) to a precise, formally notated understanding of congruence (G.CO.6). With a solid understanding of how transformations form the basis of congruence, students next examine triangle congruence criteria. Part of this examination includes the use of rigid motions to prove how triangle congruence criteria such as SAS actually work (G.CO.7, G.CO.8).