Assess students’ ability to • show and explain sequences of rigid motions and analyze different sequences of rigid motions that carry one shape to another; • explain the criteria for triangle congruence and whether given triangles are congruent or not; • understand and explain that opposite sides of a parallelogram are congruent; • explain that vertical angles are congruent; • explain that when a transversal crosses parallel lines, alternate interior and corresponding angles are congruent.
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.