Rotational Symmetry

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

• 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:  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.

• 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.