Sequences of rigid motions
• Specify sequences of rigid motions that will carry a figure onto another. • Find different ways to transform one figure into another. • Given a sequence of rigid motions, try to find a shorter sequence of rigid motions with the same outcome.
Students build on their understanding of rigid motions to formalize the definition of congruence that they developed in grade 8. They specify a series of rigid motions that carries one figure onto another and use the definition to determine whether two objects are congruent. Students show two triangles are congruent if and only if corresponding pairs of sides and angles are congruent. They explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. Armed with these criteria, students are able to prove theorems about triangles, lines, angles, and parallelograms.