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).
To find the order, imagine pinning the shape at its centre and spinning it. Count how many times it looks identical before you complete one full rotation.
Worked example
EXAMPLE
A regular pentagon is rotated about its centre. What is its order of rotational symmetry, and what angle does each rotation involve?
A regular pentagon has 5 equal sides and angles. It looks the same 5 times in one full rotation. Order = 5. Each rotation = 360° ÷ 5 = 72°; order of rotational symmetry is 5.
