Rotational symmetry
🎯 In this topic you will
- identify shapes and patterns with rotational symmetry
- describe rotational symmetry.
🧠 Key Words
- order
- rotational symmetry
Show Definitions
- order: The number of times a shape matches itself during one full turn of 360°.
- rotational symmetry: A property of a shape that allows it to fit exactly onto itself after being turned about its centre by an angle smaller than 360°.
Playground Shapes All Around
When you go to a park, you can often play on a swing, a see-saw or a roundabout. Some of the shapes you see will have line symmetry, but have you ever looked at the shapes to see which ones look the same as you turn them?
What Is Rotational Symmetry?
A shape has rotational symmetry if it can be rotated about a point to another position and still look the same.
Counting the Order
The order of rotational symmetry is the number of times the shape looks the same in one full turn. A rectangle has rotational symmetry of order 2. This button has rotational symmetry of order 4.
💡 Quick Math Tip
Half-turn check: If a shape looks the same after a half-turn, it has rotational symmetry of order 2.
❓ EXERCISES
🧠 Reasoning Tip
You can use tracing paper to help you.
$1$. Write down the order of rotational symmetry of these shapes.
👀 Show answer
a. Order $2$
b. Order $2$
c. Order $2$
d. Order $1$
e. Order $4$
f. Order $2$
$2$. Sort these cards into their correct groups.
Each group must have one blue, one green and one yellow card.
👀 Show answer
Group $1$: A Rectangle, b Order of rotational symmetry is $2$, ii
Group $2$: B Scalene triangle, c Order of rotational symmetry is $1$, i
Group $3$: C Equilateral triangle, a Order of rotational symmetry is $3$, iii
🧠 Think like a Mathematician
Read what Marcus says.
A square has 4 lines of symmetry and order 4 rotational symmetry. I think that all the special quadrilaterals have the same number of lines of symmetry as order of rotational symmetry.
Follow-up Questions:
Show Answers
- a: Marcus is not always correct. A square has 4 lines of symmetry and rotational symmetry of order 4, but other special quadrilaterals do not always have matching numbers. For example, a rectangle has 2 lines of symmetry and rotational symmetry of order 2, while a parallelogram has no lines of symmetry but rotational symmetry of order 2.
- b: No. A shape with no lines of symmetry does not always have rotational symmetry of order 1. A parallelogram has no lines of symmetry, but it has rotational symmetry of order 2.
- c: Compare examples such as a square, rectangle, rhombus and parallelogram to check whether the number of lines of symmetry matches the order of rotational symmetry in each case.
🧠 Think like a Mathematician
Choose ten capital letters from the alphabet. For example, you could choose A, E, F, H, K, L, M, N, T and Z.
Work out the number of lines of symmetry and the order of rotational symmetry of your letters.
Make a poster showing your letters; draw on any lines of symmetry and write down the order of rotation of each letter. Try and choose some letters which have the same, and some letters which have different, numbers of line symmetry and rotational symmetry.
Discuss and compare your poster with other learners in your class.
Follow-up Questions:
Show Answers
- 1: Letters such as H have two lines of symmetry and rotational symmetry of order $2$.
- 2: Letters such as A, M, and T have line symmetry but rotational symmetry of order $1$.
- 3: Letters such as H, N, and Z have rotational symmetry of order $2$.
❓ EXERCISES
$3$. Write down the order of rotational symmetry of these patterns.
👀 Show answer
a. Order $2$
b. Order $4$
c. Order $3$
$4$. Here are four different tiles.
a. Write down the order of rotation of each of the tiles.
b. Jun joins two A tiles together to make this pattern.
What is the order of rotation of the pattern?
c. Karin joins four B tiles together to make this pattern.
What is the order of rotation of the pattern?
d. Li joins two C tiles together to make this pattern.
What is the order of rotation of the pattern?
👀 Show answer
a. Tile A has order $4$, tile B has order $4$, tile C has order $2$ and tile D has order $6$.
b. The pattern has order $2$.
c. The pattern has order $4$.
d. The pattern has order $2$.