Rotational Symmetry

Table Of Contents

🎬 Math Angel Video: Rotational Symmetry Explained

What is Rotational Symmetry?

Diagram showing a square with an order of rotation symmetry 4, and explanations of the centre of rotation, angle of rotation, and order of symmetry.

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🛎️ How to Tell If a Shape Has Rotational Symmetry?

A shape has rotational symmetry if it looks the same after being rotated by an angle less than 360°.


🛎️ 3 Key Parts of Rotational Symmetry:

  • Centre of Rotation: The fixed point around which the shape is rotated.

  • Angle of Rotation: The smallest angle that makes the shape look the same as before.

  • Order of Symmetry: The number of times the shape fits onto itself in a full 360° turn.
    It is calculated as: $$ \text{Order of Symmetry} = \frac{360^\circ}{\text{Angle of Rotation}}$$

 

🛎️ Example of Rotational Symmetry:

A square has rotational symmetry because it looks the same when rotated 90 degrees.

This means its angle of rotation is 90°. Since it fits onto itself 4 times in a full 360° turn (at 90°, 180°, 270°, and 360°), its order of symmetry is 4.

Rotational Symmetry of Common Figures

Rotational symmetry of rectangle, equilateral triangle, and regular hexagon, showing their centre of rotation, angle of rotation, order of symmetry.

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  • Rectangle:
    • Angle of Rotation: 180°
    • Order of Symmetry: 2 (It fits onto itself twice in a full 360° turn at 180° and 360°).

  • Equilateral Triangle:
    • Angle of Rotation: 120°
    • Order of Symmetry: 3 (It fits onto itself three times in a full 360° turn at 120°, 240°, and 360°).

  • Regular Hexagon:
    • Angle of Rotation: 60°
    • Order of Symmetry: 6 (It fits onto itself six times in a full 360° turn at 60°, 120°, 180°, 240°, 300°, and 360°).


Rotational symmetry helps in understanding patterns, designing objects, and solving geometric problems efficiently.

Practice: Rotational Symmetry in Everyday Symbols

Illustrating three traffic signs to check for whether they have rotational symmetry, and showing different angles of rotation and orders of symmetry.

⏩️ (2:35)

  • Parking Sign:
    • No Rotational Symmetry (It never fits onto itself again in a full 360° turn except at the start).

  • Radiation Symbol:
    • Angle of Rotation: 120°
    • Order of Symmetry: 3 (It fits onto itself three times in a full 360° turn at 120°, 240°, and 360°).

  • No Entry Sign:
    • Angle of Rotation: 180°
    • Order of Symmetry: 2 (It fits onto itself twice in a full 360° turn at 180° and 360°).

🍪 Quiz: Practice Rotational Symmetry in 2D Shapes

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Rotational Symmetry

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Q: True or False: A rectangle has an angle of rotation of 180 degrees and an order of symmetry of 2.

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Q: What is the order of symmetry for an equilateral triangle?

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Q: If a figure has an angle of rotation of 120 degrees, what is its order of rotational symmetry?

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Q: A regular octagon has an order of symmetry of 8. What is the angle of rotation?

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Q: Which of the following shape has rotational symmetry?

Three signs to find the one that has rotational symmetry.

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Q: If you rotate a regular pentagon by 72 degrees, will it look the same?

A grey pentagon with a red arrow indicating a 72-degree rotation, demonstrating rotational symmetry.

Your score is

The average score is 74%

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