In this lesson, students use rigid transformations to understand the angle relationships formed by parallel lines and a transversal. This is the beginning of transformation proof, an important theme of subsequent units. By forming parallel lines with a translation, students see corresponding angles are congruent. Then they form parallel lines with a 180-degree rotation and see alternate interior angles are congruent. Students attend to precision when they use the definitions, theorems, and assertions about translations and rotations to explain why the images of certain objects are guaranteed to coincide with other objects (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.

Math Community

Today, students use sticky notes to document actions in the “Doing Math” sections of the Math Community Chart that they see or hear throughout the lesson. During the Lesson Synthesis, students share what they noticed, and then they suggest additions for the chart as part of the Cool-down. The work today continues to build a foundation for developing math community norms in a later exercise and is the start of students identifying strengths in the actions of their peers.