Unit 1, Lesson 15
Symmetry
Geometry
15.1
Warm-up
Instructional Routines
NoneMaterials
NoneActivity Narrative
This Warm-up invites students to visualize different sequences of transformations that will take a segment onto itself. This idea will be extended in subsequent activities in which students determine lines of symmetry and angles of rotation that create symmetry for various shapes. 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.
Launch
NoneActivity
NoneHere is a segment :
If we translate the segment up 5 units then down 5 units, it looks the same as it did originally.
- What other sequences of rigid transformations create an image that fits exactly over the original segment?
- Are there any single rigid motions that do the same thing?
Student Response
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Building on Student Thinking
Activity Synthesis
Select a student to share a single reflection that will take the segment onto itself, and select another student to share a single rotation that takes the segment onto itself. Tell students that if a rigid transformation exists that takes a figure onto itself, the figure is said to have symmetry. Explain that when a single reflection takes a figure onto itself, the figure has reflection symmetry and the line of reflection is called a line of symmetry of the figure. If the rotation symmetry is brought up by students, tell them that whenever a single rotation strictly greater than 0 degrees and less than 360 degrees takes a figure onto itself, the figure has rotation symmetry. This idea will be studied in more depth in a later lesson.
Student Lesson Summary
A shape has symmetry if there is a rigid transformation which creates an image that fits exactly over the original shape. A shape has reflection symmetry if there is a reflection that takes the shape to itself, and the line of reflection in this case is called a line of symmetry. A regular hexagon has many lines of symmetry. Here are 2 of them. What other lines create a reflection where the image is the same as the original figure?