Rotation Symmetry
CK-12
Kaitlyn Spong
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Printed: June 17, 2016
AUTHORS
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Kaitlyn Spong
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C HAPTER
Chapter 1. Rotation Symmetry
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Rotation Symmetry
Here you will learn about rotation symmetry and will identify shapes with rotation symmetry.
What happens when you rotate the regular pentagon below 72◦ clockwise about its center? Why is 72◦ special?
Rotation Symmetry
A shape has symmetry if it can be indistinguishable from its transformed image. A shape has rotation symmetry
if there exists a rotation less than 360◦ that carries the shape onto itself. In other words, if you can rotate a shape less
than 360◦ about some point and the shape looks like it never moved, it has rotation symmetry.
A rectangle is an example of a shape with rotation symmetry. A rectangle can be rotated 180◦ about its center and it
will look exactly the same and be in the same location. The only difference is the location of the named points.
MEDIA
Click image to the left or use the URL below.
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Solve the following problems on rotation symmetry
Does a square have rotation symmetry?
Yes, a square can be rotated 90◦ counterclockwise (or clockwise) about its center and the image will be indistinguishable from the original square.
How many angles of rotation cause a square to be carried onto itself?
Rotations of 90◦ , 180◦ and 270◦ counterclockwise will all cause the square to be carried onto itself.
Do any types of trapezoids have rotation symmetry?
No, it is not possible to rotate a trapezoid less than 360◦ in order to carry it onto itself.
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Chapter 1. Rotation Symmetry
Examples
Example 1
Earlier, you were asked why 72◦ is so special.
When you rotate the regular pentagon 72◦ about its center, it will look exactly the same. This is because the regular
pentagon has rotation symmetry, and 72◦ is the minimum number of degrees you can rotate the pentagon in order to
carry it onto itself.
Does the capital letter have rotation symmetry? If so, state the angles of rotation that carry the letter onto itself.
Example 2
Yes, it does have rotation symmetry. It can be rotated 180◦ .
Example 3
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Yes, it does have rotation symmetry. It can be rotated 180◦ .
Example 4
No, it does not have rotation symmetry.
Review
1. What does it mean for a shape to have symmetry?
2. What does it mean for a shape to have rotation symmetry?
3. Why does the stipulation of “less than 360◦ ” exist in the definition of rotation symmetry?
For each of the following shapes, state whether or not it has rotation symmetry. If it does, state the number of degrees
you can rotate the shape to carry it onto itself.
4. Equilateral triangle
5. Isosceles triangle
6. Scalene triangle
7. Parallelogram
8. Rhombus
9. Regular pentagon
10. Regular hexagon
11. Regular 12-gon
12. Regular n-gon
13. Circle
14. Kite
15. Where will the center of rotation always be located for shapes with rotation symmetry?
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 2.9.
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Chapter 1. Rotation Symmetry
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