# Lesson 20

Transformations, Transversals, and Proof

### Lesson Narrative

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. These experiences prepare students to choose a sensible translation or rotation when they prove that parallel lines cut by a transversal have alternate interior angles that are congruent and corresponding angles that are congruent in the cool-down. 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.

### Learning Goals

Teacher Facing

• Prove (in writing) that when a transversal crosses parallel lines, alternate interior angles are congruent.
• Prove that when a transversal crosses parallel lines, corresponding angles are congruent.

### Student Facing

• Let’s prove statements about parallel lines.

### Required Preparation

Prepare additional copies of the Blank Reference Chart blackline master (double-sided, 1 per student). Students can staple the new chart to their full one as they will need to continue to refer to the whole packet.

### Student Facing

• I can prove alternate interior angles are congruent.
• I can prove corresponding angles are congruent.

Building On