8.4: Rotation Symmetry
- Page ID
- 2163
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Rotation less than 360 degrees that carries a shape onto itself.
Rotational symmetry is present when a figure can be rotated (less than \(360^{\circ}\)) such that it looks like it did before the rotation. The center of rotation is the point a figure is rotated around such that the rotational symmetry holds.
For the \(H\), we can rotate it twice, the triangle can be rotated 3 times and still look the same and the hexagon can be rotated 6 times.
What if you had a six-pointed star and you rotated that star less than \(360^{\circ}\)? If the rotated star looked exactly the same as the original star, what would that say about the star?
Example \(\PageIndex{1}\)
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
Solution
The pentagon can be rotated 5 times. Because there are 5 lines of rotational symmetry, the angle would be \(\dfrac{360^{\circ}}{5}=72^{\circ}\).
Example \(\PageIndex{2}\)
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
Solution
The N can be rotated twice. This means the angle of rotation is \(180^{\circ}\).
Example \(\PageIndex{3}\)
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
Solution
The checkerboard can be rotated 4 times. There are 4 lines of rotational symmetry, so the angle of rotation is \(\dfrac{360^{\circ}}{4}=90^{\circ}\).
Example \(\PageIndex{4}\)
Find the angle of rotation and the number of times each figure can rotate.
Solution
The parallelogram can be rotated twice. The angle of rotation is \(180^{\circ}\).
Example \(\PageIndex{5}\)
Solution
The hexagon can be rotated six times. The angle of rotation is \(60^{\circ}\).
Review
- If a figure has 3 lines of rotational symmetry, it can be rotated _______ times.
- If a figure can be rotated 6 times, it has _______ lines of rotational symmetry.
- If a figure can be rotated n times, it has _______ lines of rotational symmetry.
- To find the angle of rotation, divide \(360^{\circ}\) by the total number of _____________.
- Every square has an angle of rotation of _________.
Determine whether each statement is true or false.
- Every parallelogram has rotational symmetry.
- Every figure that has line symmetry also has rotational symmetry.
Determine whether the words below have rotation symmetry.
- OHIO
- MOW
- WOW
- KICK
- pod
Find the angle of rotation and the number of times each figure can rotate.
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Figure \(\PageIndex{12}\) -
Figure \(\PageIndex{13}\) -
Figure \(\PageIndex{14}\)
Determine if the figures below have rotation symmetry. Identify the angle of rotation.
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Figure \(\PageIndex{15}\) -
Figure \(\PageIndex{16}\) -
Figure \(\PageIndex{17}\)
Review (Answers)
To see the Review answers, open this PDF file and look for section 12.2.
Vocabulary
| Term | Definition |
|---|---|
| rotational symmetry | When a figure can be rotated (less than 360^{\circ}\)) such that it looks like it did before the rotation. The center of rotation is the point a figure is rotated around such that the rotational symmetry holds. |
| Center of Rotation | In a rotation, the center of rotation is the point that does not move. The rest of the plane rotates around this fixed point. |
| Rotation | A rotation is a transformation that turns a figure on the coordinate plane a certain number of degrees about a given point without changing the shape or size of the figure. |
| Rotation Symmetry | A figure has rotational symmetry if it can be rotated less than \(360^{\circ}\) around its center point and look exactly the same as it did before the rotation. |
| Symmetry | A figure has symmetry if it can be transformed and still look the same. |
Additional Resources
Interactive Element
Video: Rotation Symmetry Principles - Basic
Activities: Rotation Symmetry Discussion Questions
Study Aids: Symmetry and Tessellations Study Guide
Practice: Rotation Symmetry
Real World: This End Up