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Rotation Symmetry
When looking at an image or shape, we say that the shape has a rotation symmetry if the shape can be rotated (spun or turned) around a point less than a full circle to end up with the original shape.
- The centre of rotation is the point which we rotate the shape around
- The order of rotation is the number of times we end up with the original shape when rotating it in a full circle
- The angle of rotation is the smallest angle we need to rotate the shape to end up with the original shape
- We can write this in degrees or as a fraction of a turn
Example
If we know that the order of rotation of a shape is 4, that means that if we rotate the shape a full circle, we will see the original shape
4
times.In this case, what is the angle of rotation?
90 degrees
Write it Down
The order and angle of rotation are related!
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Example: Rotation Symmetry
a) What type of symmetry does the above figure have?
It has both line and rotation symmetry.
b) If it has line symmetry, how many and what type of line symmetry does it have?
It has 7 lines of symmetry, they are vertical and oblique lines of symmetry.
c) If it has rotation symmetry, what is the order and angle of rotation?
We can rotate this shape around the centre of the shape, and everytime we rotate it so that the pointy corner (vertex) gets to the spot of the next corner, we will see the original shape. Since there are 7 pointy corners, we know that the order of rotation is 7 -- meaning that we will see the same shape 7 times if we rotate it in a full circle.
The angle of rotation is .
So, the angle of rotation is approximately or turn.
Practice: Rotation Symmetry
Select all of the types of symmetry that this figure has.