Lesson objective: Understand that rigid transformations can be described using the coordinates, and that the transformed figures are congruent to the original.

Students bring prior knowledge of transformation types from 8.G.1. This prior knowledge is extended to include features of the coordinate plane as students describe the transformations using coordinates. A conceptual challenge students may encounter is the needed items for a complete description in each type of rigid transformation.

The concept is developed through work with a drawing in the coordinate plane, which the students have to prove has been reproduced using a rigid transformation in the coordinate plane.

This work helps students deepen their understanding of equivalence because rigid transformations always result in figures congruent to their preimages.

Students engage in Mathematical Practice 6 (Attend to Precision) as they include the necessary information required for describing a transformation using coordinates. The characters in the lesson provide guidance to help students avoid common errors in understanding the difference between reflections and rotations.

**Key vocabulary:**

- center of rotation
- line of reflection
- origin
- reflect
- rotate
- translate

**Special materials needed:**

- patty paper (optional)
- transparency with wet- or dry-erase marker (optional alternative to the patty paper)