Deepen your understanding of symmetry by combining line and rotational symmetry, and exploring symmetry in real-world designs.
Many shapes have both types of symmetry at once. A regular polygon with n sides always has n lines of symmetry and rotational symmetry of order n.
A regular hexagon has how many lines of symmetry, and what order of rotational symmetry?
6 lines of symmetry, and rotational symmetry of order 6
Does a rectangle (not a square) have rotational symmetry? If so, what order?
Yes, order 2 — it looks the same after a 180° rotation
Symmetry appears throughout nature, architecture, and logos. Recognizing the type and order of symmetry in a design helps analyze how it was constructed.
A wheel with 8 evenly spaced spokes has what order of rotational symmetry?
8, since rotating by 45° (360°÷8) brings it back to looking the same
Why do many company logos use rotational symmetry rather than only line symmetry?
Rotational symmetry often looks more dynamic and modern, and works well when a logo needs to look balanced from multiple angles
1. A regular octagon has how many lines of symmetry, and what order of rotational symmetry?
2. Does an equilateral triangle have both line and rotational symmetry?
3. A wheel with 6 evenly spaced spokes has what order of rotational symmetry?
4. Does a parallelogram (that isn't a rectangle or rhombus) have any line symmetry?
5. A regular pentagon has how many lines of symmetry?