Lesson plan

Lesson 20: Transformations, Transversals, and Proof

teaches Alabama State Standards Geo-31.a.
teaches Alabama State Standards Geo-31.
teaches Arizona State Standards G.G-CO.C.9
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards HSG-CO.C.9 http://corestandards.org/Math/Content/HSG/CO/C/9
teaches Common Core State Standards HSG-CO.A.2 http://corestandards.org/Math/Content/HSG/CO/A/2
teaches Common Core State Standards HSG-CO.A.1 http://corestandards.org/Math/Content/HSG/CO/A/1
teaches Colorado State Standards HS.G-CO.C.9.
teaches Georgia State Standards MGSE9-12.G.CO.9.
teaches Kansas State Standards G.CO.7.
teaches Minnesota State Standards 9.3.3.2.
teaches Minnesota State Standards 9.3.3.1.
teaches Minnesota State Standards 9.3.2.4.
teaches Minnesota State Standards 9.3.2.2.
teaches Minnesota State Standards 9.3.2.1.
teaches Ohio State Standards G.CO.9.
teaches Ohio State Standards G.CO.1.
teaches Pennsylvania State Standards CC.2.3.HS.A.3.
teaches Pennsylvania State Standards CC.2.3.HS.A.1.

Lesson 20: Transformations, Transversals, and Proof

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.

Lesson overview

  • 20.1 Warm-up: 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 Cool-down: 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 (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.

Standards:

  • This lesson builds on the standards:CCSS.8.G.A.5MS.8.G.5MO.8.GM.A.5cCCSS.HSG-CO.A.4MS.G-CO.4MO.G.CO.A.4
  • This lesson builds towards the standard:CCSS.HSG-CO.C.10MS.G-CO.10MO.G.CO.C.9

 

 

 

 

 

IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.