12.2: Rotation Symmetry
What if you were asked to consider the presence of symmetry in nature? The starfish, below, is one example of symmetry in nature. Draw in the center of symmetry and the angle of rotation for this starfish. After completing this Concept, you'll be able to answer questions like these.
Watch This
CK-12 Foundation: Chapter12RotationSymmetryA
Brightstorm: Rotational Symmetry
Guidance
Rotational Symmetry is when a figure can be rotated (less that \begin{align*}360^\circ\end{align*}
Example A
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
The pentagon can be rotated 4 times and show rotational symmetry. Because there are 5 lines of rotational symmetry, the angle would be \begin{align*}\frac{360^\circ}{5}= 72^\circ\end{align*}
Example B
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
The \begin{align*}N\end{align*}
Example C
Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.
The checkerboard can be rotated 3 times. There are 4 lines of rotational symmetry, so the angle of rotation is \begin{align*}\frac{360^\circ}{4}=90^\circ\end{align*}
Watch this video for help with the Examples above.
CK-12 Foundation: Chapter12RotationSymmetryB
Concept Problem Revisited
The starfish has rotational symmetry of \begin{align*}72^\circ\end{align*}
Vocabulary
Rotational symmetry is present when a figure can be rotated (less than \begin{align*}360^\circ\end{align*}
Guided Practice
Find the angle of rotation and the number of times each figure can rotate.
1.
2.
3.
Answers:
1. The parallelogram can be rotated twice. The angle of rotation is \begin{align*}180^\circ\end{align*}
2. The hexagon can be rotated six times. The angle of rotation is \begin{align*}60^\circ\end{align*}
3. This figure can be rotated four times. The angle of rotation is \begin{align*}90^\circ\end{align*}
Practice
- 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 \begin{align*}n\end{align*}
n times, it has _______ lines of rotational symmetry. - To find the angle of rotation, divide \begin{align*}360^\circ\end{align*}
360∘ 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.
Determine if the figures below have rotation symmetry. Identify the angle of rotation.
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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 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.Image Attributions
Here you'll learn how to determine whether or not a shape has rotation symmetry.