Lesson 15
Symmetry
Lesson Narrative
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).
Learning Goals
Teacher Facing
 Describe (orally and in writing) the reflections that take a figure onto itself.
Student Facing
 Let’s describe some symmetries of shapes.
Required Materials
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.)
Learning Targets
Student Facing
 I can describe the reflections that take a figure onto itself.
CCSS Standards
Glossary Entries

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).
Print Formatted Materials
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Student Task Statements  docx  
Cumulative Practice Problem Set  docx  
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Teacher Presentation Materials  docx  
Blackline Masters  zip 