Rotational symmetry questions with answers

Questions

1. Question 1Order of rotational symmetry

   The diagram shows the letter U. Write down its order of rotational symmetry.

   Show the worked solution

   1. Step 1: Turn the shape about its centre: in one full turn, how many times does it look exactly the same?It looks the same only after a full turn.$\text{Order} = 1$
2. Question 2Order of rotational symmetry

   The diagram shows an isosceles triangle. Write down its order of rotational symmetry.

   Show the worked solution

   1. Step 1: Turn the shape about its centre: in one full turn, how many times does it look exactly the same?It looks the same only after a full turn.$\text{Order} = 1$
3. Question 3Angle of rotation

   The diagram shows a regular nonagon. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

   Show the worked solution

   1. Step 1: Turn the shape about its centre: in one full turn, how many times does it look exactly the same?It looks the same every ninth of a turn.$\text{Order} = 9$
   2. Step 2: Share the full turn equally$\text{Angle} = \dfrac{360^\circ}{9}$$\text{Angle} = 40^\circ$
4. Question 4Angle of rotation

   The diagram shows a propeller shape. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

   Show the worked solution

   1. Step 1: Turn the shape about its centre: in one full turn, how many times does it look exactly the same?It looks the same every third of a turn.$\text{Order} = 3$
   2. Step 2: Share the full turn equally$\text{Angle} = \dfrac{360^\circ}{3}$$\text{Angle} = 120^\circ$