# Lesson 8

Rotation Patterns

### Lesson Narrative

In this lesson, rigid transformations are applied to line segments and triangles. For line segments, students examine the impact of a 180 degree rotation. This is important preparatory work for studying parallel lines and rigid transformations, the topic of the next lesson. For triangles students look at a variety of transformations where rotations of 90 degrees and 180 degrees are again a focus. This work and the patterns that students build will be important later when they study the Pythagorean Theorem.

Throughout the lesson, students use the properties of rigid transformations (they do not change distances or angles) in order to make conclusions about the objects they are transforming (MP7).

### Learning Goals

Teacher Facing

• Draw and label rotations of 180 degrees of a line segment from centers of the midpoint, a point on the segment, and a point not on the segment.
• Generalize (orally and in writing) the outcome when rotating a line segment 180 degrees.
• Identify(orally and in writing) the rigid transformations that can build a diagram from one starting figure.

### Student Facing

Let’s rotate figures in a plane.

### Student Facing

• I can describe how to move one part of a figure to another using a rigid transformation.

Building Towards

### Glossary Entries

• corresponding

When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.

For example, point $$B$$ in the first triangle corresponds to point $$E$$ in the second triangle. Segment $$AC$$ corresponds to segment $$DF$$.

• rigid transformation

A rigid transformation is a move that does not change any measurements of a figure. Translations, rotations, and reflections are rigid transformations, as is any sequence of these.