Line and rotational symmetry · Usually met around P6
Rotational symmetry
Smallest turn = 360° ÷ the order.
How to do it
Method
Smallest turn = 360° ÷ the order
A square matches 4 times: 360 ÷ 4 = 90°
Another way
Trace and turn
Pin the centre, turn, count the matches
In full
Turn a shape about its centre: if it matches itself before a whole turn (360°), it has rotational symmetry. The number of times it matches in one whole turn is its order: a square matches at 90°, 180°, 270° and 360°, 4 times. The smallest turn = 360° ÷ the order: a square 360 ÷ 4 = 90°; a regular hexagon 360 ÷ 6 = 60°. A parallelogram matches after 180° but has no line of symmetry — turning and folding are different things. To finish a shape with rotational symmetry, turn the part you have about the centre again and again, drawing it each time — don't flip it as in a mirror. Another way: trace it on thin paper, pin the centre and turn it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
What is the smallest turn about its centre, in degrees, that makes this shape match itself?
Show the answer and working
Answer: 180°
It matches 2 times in a whole turn: 360 ÷ 2 = 180°.
Example 2
This shape has rotational symmetry.
True or false?
Show the answer and working
Answer: False
It has rotational symmetry only if it matches before a whole turn; this one matches 1 times in one turn.
Example 3
A regular polygon has 6 sides. What is the smallest turn about its centre, in degrees, that makes it match itself?
Show the answer and working
Answer: 60°
It matches 6 times in a whole turn: 360 ÷ 6 = 60°.
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