Lesson plan

Lesson 10: Composing Figures

teaches Alabama State Standards 8-23.
teaches Alabama State Standards 8-22.
teaches Arizona State Standards 8.G.A.1
teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards 8.G.A.1.a http://corestandards.org/Math/Content/8/G/A/1/a
teaches Common Core State Standards 8.G.A.1.b http://corestandards.org/Math/Content/8/G/A/1/b
teaches Colorado State Standards 8.G.A.1.
teaches Georgia State Standards MGSE8.G.1.
teaches New York State Standards NY-8.G.1b.
teaches New York State Standards NY-8.G.1a.
teaches Pennsylvania State Standards CC.2.3.8.A.2.

Lesson 10: Composing Figures

In this lesson, students create composite shapes using translations, rotations, and reflections of polygons and continue to observe that the side lengths and angle measures do not change. They use this understanding to draw conclusions about the composite shapes. Later, they will use these skills to construct informal arguments, for example about the sum of the angles in a triangle.

When students rotate around a vertex or reflect across the side of a figure, it is easy to lose track of the center of rotation or line of reflection since they are already part of the figure. It can also be challenging to name corresponding points, segments, and angles when a figure and its transformation share a side. Students attend to these details carefully in this lesson (MP6).

Consider using the optional activity if you need to reinforce students’ belief that rigid transformations preserve distances and angle measures after main activities.

Lesson overview

  • 10.1 Warm-up: Angles of an Isosceles Triangle (10 minutes)
  • 10.2 Activity: Triangle Plus One (10 minutes)
    • Includes "Are you Ready for More?" extension problem
  • 10.3 Activity: Triangle Plus Two (15 minutes)
  • 10.4 Optional Activity: Triangle ONE Plus (10 minutes)
  • Lesson Synthesis
  • 10.5 Cool-down: Identifying Side Lengths and Angle Measures (5 minutes)

Learning goals:

  • Draw and label images of triangles under rigid transformations and then describe (orally and in writing) properties of the composite figure created by the images.
  • Generalize that lengths and angle measures are preserved under any rigid transformation.
  • Identify side lengths and angles that have equivalent measurements in composite shapes and explain (orally and in writing) why they are equivalent.

Learning goals (student facing):

  • Let’s use reasoning about rigid transformations to find measurements without measuring.

Learning targets (student facing):

  • I can find missing side lengths or angle measures using properties of rigid transformations.

Required materials:

  • geometry toolkits


  • Access the complete Grade 8 glossary.






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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