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10.2.3 Rotation symmetry
A shape has rotation symmetry when it still iooks the same after a rotation (of less
than one full turn). The order of rotation symmetry, is the number of times a shape
fits onto itself in one full turn.
Example 1
Q Does this shape have rotation symmetry?
If yes, what is its order of rotation symmetry?
Solution
If this star is rotated about its centre point, it will
look the same in five different positions.
B D
D C D C
Position 1 Position 2 Position 3 Position 4 Position 5 Back to
position 1
This star shape can be rotated to five different positions and still look the same as the
figure in the original position. We say it has a rotation symmetry of order 5.
P Spotlight Q Does this shape have rotation symmetry?
if yes, what is the order of rotation symmetry?
This symbol for recycling Solution
has rotational symmetry
of order 3.
L,. This right-angled, scalene triangle has no rotation symmetry. The shape cannot
be rotated into a different position and still look the same. It looks the same only
once in one full turn.
Investigate!
m
Find an image of an airplane propeller. Trace its
shape on a piece of tracing paper. Place your tracing
directly over the propeller. Use a pin to pin down
Draw a shape with 2 lines the tracing in the centre of the propeller. Rotate it.
of symmetry and rotational e Make a 30^ 60°, 90°, 120° turn.
symmetry of order 2.
e The tracing fits onto itself after a turn.
How many such turns can you make
before the tracing moves back to its original position? What is the order of
rotational symmetry of the propeller about its centre?
UNIT 10 I Shapes and Symmetry
