Lesson 9

Composing Figures

Lesson Narrative

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.

Learning Goals

Teacher Facing

  • 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.

Student Facing

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

Required Materials

Learning Targets

Student Facing

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

CCSS Standards


Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In