Acc7.1 Rigid Transformations and Congruence

In this unit, students learn to understand and use the terms “reflection,” “rotation,” and “translation,” recognizing what determines each type of transformation. For example, two points determine a translation. They learn to understand and use the terms “transformation” and “rigid transformation.” They identify and describe translations, rotations, reflections, and sequences of these, using the terms “corresponding sides” and “corresponding angles,” and recognizing that lengths and angle measures are preserved. They draw images of figures under rigid transformations on and off square grids and the coordinate plane. They use rigid transformations to generate shapes and to reason about measurements of figures. They learn to understand congruence of plane figures in terms of rigid transformations. They recognize when one plane figure is congruent or not congruent to another. They use the definition of “congruent” and properties of congruent figures to justify claims of congruence or non-congruence. They investigate whether sets of angle and side length measurements determine unique triangles, multiple triangles, or fail to determine triangles. Students also study and apply angle relationships, learning to understand and use the terms “complementary,” “supplementary,” “vertical angles,” and “unique.”