Translations, reflections, and rotations are all examples of rigid motions that you have studied in the past. Here, you will formalize the definitions of these transformations and learn how to perform transformations and sequences of transformations with geometry software. You will also learn what it means for a shape to have reflection or rotation symmetry.
You looked at different types of transformations. Rigid transformations were those that preserved distance and angles. Some transformations, such as stretches, were not rigid transformations.
You formalized the definitions of translations, reflections, and rotations using vectors, circles, and parallel and perpendicular lines. You also learned how to use Geogebra to perform transformations and composite transformations. You saw that when a shape could be reflected across a line and be carried onto itself it had reflection symmetry. When a shape could be rotated less than 360∘ about a point and be carried onto itself it had rotation symmetry.
A solid understanding of rigid transformations will inform your formal understanding of triangle congruence and proof.