Symmetries of Shapes

Rotations and flips

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A symmetry is a move that leaves a shape looking the same.
• A regular $n$-gon has $2n$ symmetries: $n$ rotations and $n$ reflections.
• Every symmetry of a square can be built from one rotation and one flip.

Steps

1. What is a symmetry?
2. Match the target
3. Count them
4. All eight moves
5. Hexagons
6. Turning a cube
7. A trickier target