# Lesson 14

Defining Rotations

### Lesson Narrative

The purpose of this lesson is to develop a rigorous definition of rotation, building on what students know from previous courses. Students first focus on what information is important for defining a rotation and then determine properties of rotations by rotating segments to make isosceles triangles. Students attend to precision when they clarify what information they need to uniquely determine a given rotation (MP6).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

### Learning Goals

Teacher Facing

• Comprehend that the term "rotation" (in written and spoken language) requires several descriptors including angle, center, and direction.
• Determine whether a figure is a rotation of another.
• Draw rotations of figures.

### Student Facing

• Let’s rotate shapes precisely.

### Student Facing

• I can describe a rotation by stating the center and angle of rotation.
• I can draw rotations.

Building On

Building Towards

### Glossary Entries

• rotation

A rotation has a center and a directed angle. It takes a point to another point on the circle through the original point with the given center. The 2 radii to the original point and the image make the given angle.

$$P'$$ is the image of $$P$$ after a counterclockwise rotation of  $$t^\circ$$ using the point $$O$$ as the center.

​​​​​Quadrilateral $$ABCD$$ is rotated 120 degrees counterclockwise using the point $$D$$ as the center.