Rotational symmetry and order of symmetry

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.