Rotational symmetry

Key Notes:

What is Rotational Symmetry?

  • A shape has rotational symmetry if it looks the same after being turned (rotated) around a center point.

Center of Rotation:

  • This is the fixed point around which the shape is rotated.

Angle of Rotation:

  • The number of degrees a shape is turned. Common angles are 90°, 180°, 270°, and 360°.

Order of Rotational Symmetry:

  • The number of times a shape fits onto itself in one full turn (360°).
  • 👉 Example: A square has order 4 rotational symmetry.

Examples of Rotational Symmetry:

  • Circle – infinite rotational symmetry
  • Square – order 4
  • Equilateral triangle – order 3
  • Rectangle – order 2

No Rotational Symmetry:

  • Some shapes only match their original position after a 360° turn. These shapes have no rotational symmetry or order 1.

Real-Life Examples:

  • Steering wheel, fan blades, flowers, and spinning tops often show rotational symmetry.

Why is it important?

  • Helps in understanding geometry, art, design, and patterns in the real world.

Learn with an example

🎯 Does this picture have rotational symmetry?

  • yes
  • no

If you rotate this picture 1/2 turn or less, it will not look exactly the same.

This picture does not have rotational symmetry.

🎯 Does this picture have rotational symmetry?

  • yes
  • no

If you rotate this picture 1/2 turn or less, it will not look exactly the same.

This picture does not have rotational symmetry.

🎯 Does this picture have rotational symmetry?

  • yes
  • no

If you rotate this picture 1/2 turn or less, it will not look exactly the same.

This picture does not have rotational symmetry.

let’s practice!