The purpose of this lesson is for students to apply the property that rigid transformations preserve angle measures and side lengths. In this lesson, students create composite shapes using translations, rotations, and reflections of polygons and continue to observe that the side lengths and angle measures do not change. They use this understanding to draw conclusions about the composite shapes. Students apply the property that the image of a line segment under a rotation about a point not on the line is parallel to the original segment in order to explain why a figure must be a parallelogram. Students use the structure of rigid transformations as they apply these properties to various figures (MP7).

Students also create a drawing of a composite figure using rigid transformations, then make observations about the corresponding angle measures and side lengths. They identify corresponding parts and explain why they must be the same length or measure.

Consider using the optional activity to reinforce students’ belief that rigid transformations preserve distances and angle measures.