1. GCSE/KS3 :: Rotational Symmetry
Fundamentals
GCSE/KS3 :: Rotational Symmetry
@DrFrostMaths
Objectives: Be able to identify the order of rotational symmetry.
Last modified: 15th January 2020

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3. Click for Fro-manimation
Rotational Symmetry
Rotate this shape by 180°. What do you notice?
Click for Fro-manimation
You get the same shape!
If you rotate a shape and see the same thing before you spin the shape a full way round, it is said to have rotational symmetry.

4. Identifying the order of rotational symmetry
We initially spin the shape once to see the same shape.
(Ignoring the circle!)
We say the order of rotational symmetry is 2, because we span it 2 times before we got back to where we started.
Spinning a second time gets us back to where we started.
! The order of rotational symmetry of a shape is the number of times we can spin the shape to see the same, until we’ve done a full spin.

5. 5 1 Further Examples ? ? Order of rotational symmetry:
We will only see the same shape after doing a full spin.
Fro Tip: If a shape has no rotational symmetry, then the order of rotational symmetry is 1 (and not 0).

6. Mini Exercise
Identify the order of rotational symmetry and the number of lines of symmetry for each shape.
Order of rotational symmetry
Number of lines of symmetry ? ? 2 2 ? ? 2 ? ? 1 1 ? ? 4 4

7. 2 Exercise ? Reveal (on printed worksheet) 1
[OCR GCSE(9-1) Nov F Q1b] Here is a hexagon.
Write down the order of rotation symmetry of the hexagon.
? Reveal 2

8. 3 Exercise ? Reveal (on printed worksheet) 2
[Edexcel GCSE June2010-2F Q10c] Here is a shape. Write down the order of rotational symmetry of this shape.
? Reveal 3

9. 4 Exercise ? Reveal (on printed worksheet) 3
[OCR GCSE June F Q5a] What is the order of rotation symmetry of this shape?
? Reveal 4

10. 8 Exercise ? Reveal (on printed worksheet) 4
[OCR GCSE(9-1) June F Q1b] Write down the order of rotation symmetry of this regular octagon.
? Reveal 8

11. B and C Exercise ? Reveal (on printed worksheet) 5
[Edexcel GCSE June2006-2F Q13b Edited] Here are 5 shapes.
Two of these shapes have rotational symmetry of order 2. Select the letters of these two shapes.
? Reveal
B and C

12. B and D Exercise ? Reveal (on printed worksheet) 6
[Edexcel GCSE March2012-2F Q8b]
Here are five shapes.
Two of these shapes have rotational symmetry of order 2
Write down the letter of each of these two shapes.
? Reveal
B and D

13. A Exercise ? Reveal (on printed worksheet) 7
[Edexcel GCSE June F Q11bi] Here are four road signs.
Only one of these four road signs has rotational symmetry. Select the letter of this road sign.
? Reveal A

14. 2 Exercise ? Reveal (on printed worksheet) 8
[Edexcel GCSE June2013-1F Q21b] The diagrams show patterns made from grey tiles and white tiles.
Write down the order of rotational symmetry of pattern C.
? Reveal 2

15. B Exercise ? Reveal (on printed worksheet) 9
[AQA GCSE June F Q4c]
Here are five flags.
Which flag has rotational symmetry but not line symmetry?
? Reveal B

16. Exercise ? ? ? ? 𝐴𝐵 is parallel to 𝐷𝐶. T Angle 𝐴 = Angle 𝐶.
(on printed worksheet) 10
[AQA GCSE Jan F Q5 Edited] Here is a parallelogram.
Write T for True or F for False for each of the statements below.
𝐴𝐵 is parallel to 𝐷𝐶. T
Angle 𝐴 = Angle 𝐶.
The parallelogram has 2 lines of symmetry. F
The parallelogram has rotational symmetry of order 2. ? ? ? ?

17. Exercise ? Reveal (on printed worksheet) N1
[JMC 2011 Q15] What is the smallest number of additional squares which must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?
? Reveal

18. Exercise ? Reveal (on printed worksheet) N2
[JMC 2016 Q16] Each of the nine small squares in this grid can be coloured completely black or completely white.
What is the largest number of squares that can be coloured black so that the design created has rotational symmetry of order 2, but no lines of symmetry?
? Reveal