Lesson 20: Transformations, Transversals, and Proof
About this lesson
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 cooldown. 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.
Lesson overview
 20.1 Warmup: Math Talk: Angle Relationships (5 minutes)

20.2 Activity: Make a Mark? Give a Reason. (15 minutes)
 Digital applet in this activity

20.3 Activity: An Alternate Explanation (10 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 20.4 Cooldown: Transformations on Parallel Lines (10 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s prove statements about parallel lines.
Learning targets (student facing):
 I can prove alternate interior angles are congruent.
 I can prove corresponding angles are congruent.
Required materials:
 copies of blackline master
Required preparation:
 Prepare additional copies of the Blank Reference Chart blackline master (doublesided, 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.
Standards:
 This lesson builds on the standards:CCSS.8.G.A.5MS.8.G.5MO.8.GM.A.5cCCSS.HSGCO.A.4MS.GCO.4MO.G.CO.A.4
 This lesson builds towards the standard:CCSS.HSGCO.C.10MS.GCO.10MO.G.CO.C.9
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