Rotational Symmetry
Grade 2Rotating into itself
Rotational symmetry is when a shape looks exactly the same after a rotation of less than 360°. The number of times it looks the same in one full turn is the order of rotational symmetry.
Every shape has rotational symmetry of order at least 1 (a full 360° turn). We only say a shape has rotational symmetry when the order is 2 or more.
Orders for common shapes
Square: order 4 (looks the same every 90°). Rectangle: order 2. Regular hexagon: order 6. Equilateral triangle: order 3. Parallelogram: order 2. Scalene triangle: order 1 (none).
Worked example
Try this one
A square has both reflective and rotational symmetry.
(a) State the number of lines of symmetry and the order of rotational symmetry of a square. [2]
(b) A student claims that any shape with \( 4 \) lines of symmetry must have rotational symmetry of order \( 4 \). Explain, with reference to the square, why the order of rotational symmetry of a regular shape equals its number of lines of symmetry. [1]
Recall the symmetry of a square, then think about why the two kinds of symmetry match for regular shapes.
Ask yourself: 'how do the equally spaced mirror lines relate to equally spaced turning positions?' Consider that each mirror line and each rotation share the same centre and equal spacing.
