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Rotation Symmetry

When a figure can be rotated less than 360 degrees and look the same as it did before.

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Rotation Symmetry

What if you 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? After completing this Concept, you'll be able to determine if a figure like this one has rotational symmetry.

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Rotation Symmetry CK-12

Guidance

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.

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 5 times. Because there are 5 lines of rotational symmetry, the angle would be \frac{360^\circ}{5}= 72^\circ .

Example B

Determine if the figure below has rotational symmetry. Find the angle and how many times it can be rotated.

The N can be rotated twice. This means the angle of rotation is 180^\circ .

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 4 times. There are 4 lines of rotational symmetry, so the angle of rotation is \frac{360^\circ}{4}=90^\circ .

Rotation Symmetry CK-12

Guided Practice

Find the angle of rotation and the number of times each figure can rotate.

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2.

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Answers:

1. The parallelogram can be rotated twice. The angle of rotation is 180^\circ .

2. The hexagon can be rotated six times. The angle of rotation is 60^\circ .

3. This figure can be rotated four times. The angle of rotation is 90^\circ .

Practice

  1. If a figure has 3 lines of rotational symmetry, it can be rotated _______ times.
  2. If a figure can be rotated 6 times, it has _______ lines of rotational symmetry.
  3. If a figure can be rotated n times, it has _______ lines of rotational symmetry.
  4. To find the angle of rotation, divide 360^\circ by the total number of _____________.
  5. Every square has an angle of rotation of _________.

Determine whether each statement is true or false.

  1. Every parallelogram has rotational symmetry.
  2. Every figure that has line symmetry also has rotational symmetry.

Determine whether the words below have rotation symmetry.

  1. OHIO
  2. MOW
  3. WOW
  4. KICK
  5. 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.

Vocabulary

rotational symmetry

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

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

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

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

Symmetry

A figure has symmetry if it can be transformed and still look the same.

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