Symmetry · Grade 6
In Grade 6 you learn: rotational symmetry.
A shape has line symmetry if it can be folded so that the two halves match exactly. It has rotational symmetry if it looks the same after a turn of less than 360°. Symmetry appears in logos, flowers, snowflakes and road signs.
Key facts
- The order of rotational symmetry is how many times a shape fits onto itself in one full turn (order 1 means no rotational symmetry).
- A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
- Square 4 lines; rectangle 2; rhombus 2; kite 1; parallelogram 0 (but order 2).
- The smallest turn that fits a shape onto itself is 360° ÷ order.
Worked examples
Example 1
What is the order of rotational symmetry of a parallelogram?
Answer: 2
Example 2
A regular octagon has rotational symmetry of order 8. What is the smallest turn that fits it onto itself, and how many lines of symmetry does it have?
Answer: 45°; 8 lines of symmetry