Rotational symmetry and order of symmetry

Decide whether a shape or picture has reflective (line) symmetry, count how many axes of symmetry it has, and state its order of rotational symmetry -- then describe all of a figure's symmetries together in one answer.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM6-9
New NZC (2026)
  • NZC26-P4-GEO-SPR-K-Y9-01

Resources

Terminology

  • symmetry
  • line of symmetry
  • axis of symmetry
  • reflective symmetry
  • mirror line
  • vertical line of symmetry
  • horizontal line of symmetry
  • rotational symmetry
  • order of rotational symmetry
  • centre of rotation
  • angle of rotation
  • full turn (360 degrees)
  • asymmetric

Task goals

  • Decide whether a picture or shape has a vertical line of symmetry, and say so with a yes or no.
  • Decide whether a figure has a horizontal line of symmetry, or any line of symmetry at all, when the mirror line is not given.
  • State the order of rotational symmetry of a shape or everyday object, including recognising order 1 when a figure only maps onto itself after a full turn.
  • Count the total number of axes of symmetry of a figure, and recognise that a circle has infinitely many.
  • Determine the order of rotational symmetry of regular and composite figures such as a cross, an eight-pointed star, a regular octagon, and a six-toothed cog.
  • Describe all the symmetries of a figure in a single answer, giving both the number of lines of symmetry and the order of rotational symmetry.
  • Justify whether an irregular or everyday object has any symmetry, explaining what feature makes it symmetric or asymmetric.

Where this fits

What leads into this objective, and where it goes next.

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Rotational symmetry and order of symmetry

Rotational symmetry and order of symmetry

Know

A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.

Statement▸
Year 9 · Geometry · Spatial reasoning
NZC26-P4-GEO-SPR-K-Y9-01

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