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Lesson plan

Lesson 15: Symmetry

teaches Common Core State Standards HSG-CO.A.3 http://corestandards.org/Math/Content/HSG/CO/A/3
teaches Common Core State Standards HSG-CO.A.2 http://corestandards.org/Math/Content/HSG/CO/A/2
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7

Lesson 15: Symmetry

In this lesson and the next, students determine the cases where applying a certain rigid motion to a shape doesn’t change it. This is the idea of symmetry. A shape is said to have symmetry if there is a rigid transformation that takes the shape to itself. Students first study reflection symmetry using lines of symmetry, and then they study rotation symmetry in a subsequent lesson. Translation symmetry isn’t mentioned explicitly, but students were exposed to the idea that a line has translation symmetry in a previous lesson. Students apply their understanding of rigid transformations to identify shapes where there is a line of symmetry which reflects the shape onto itself, satisfying the definition of reflection symmetry. The fact that reflecting a segment across its perpendicular bisector exchanges its endpoints will be useful in the next unit when students study triangle congruence.

In one activity, each group is assigned a different shape to consider. Students make use of structure when they discuss which lines of symmetry apply to a type of shape generally, rather than limiting their thinking to a given example (MP7).

Lesson overview

  • 15.1 Warm-up: Back to the Start (5 minutes)
  • 15.2 Activity: Self Reflection (20 minutes)
    • Includes "Are you Ready for More?" extension problem
  • 15.3 Activity: Diabolic Diagonals (10 minutes)
  • Lesson Synthesis
  • 15.4 Cool-down: Criss Cross (5 minutes) 

Learning goals:

  • Describe (orally and in writing) the reflections that take a figure onto itself.

Learning goals (student facing):

  • Let’s describe some symmetries of shapes.

Learning targets (student facing):

  • I can describe the reflections that take a figure onto itself.

Required materials:

  • Copies of blackline master
  • Geometry toolkits
  • Sticky notes
  • Tools for creating a visual display

Required preparation:

  • Print and cut up slips from the blackline master.
  • The blackline master for this lesson contains 8 different shapes.
  • Each group of 2–4 students will be investigating a shape.
  • Prepare enough copies of the blackline master so that each student in each group gets a copy of the shape their group will investigate. (Note: Students will repeat this process for rotation symmetry in the next lesson; it may be easier to prepare twice as many shapes once rather than repeat the process.)


  • line of symmetry - A line of symmetry for a figure is a line such that reflection across the line takes the figure onto itself.

The figure shows two lines of symmetry for a regular hexagon, and two lines of symmetry for the letter I.

  • reflection symmetry - A figure has reflection symmetry if there is a reflection that takes the figure to itself.

  • symmetry - A figure has symmetry if there is a rigid transformation which takes it onto itself (not counting a transformation that leaves every point where it is).
  • Access the complete Geometry Course glossary.


  • This lesson builds on the standards:CCSS.8.G.A.1MS.8.G.1MO.8.GM.A.1aMO.8.GM.A.1bCCSS.HSG-CO.A.4MS.G-CO.4MO.G.CO.A.4






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