A circle looks the same when turned
Turn a round plate by any amount. It looks just as it did before.
The rule
Turn a shape about its centre. If it then looks exactly the same, it fits itself. That turn is a rotational symmetry.
Rule: A circle looks the same after any turn about its centre.
Fold a shape along a line. If both halves match, the line is a line of reflection symmetry. It is also called a mirror line.
Every diameter of a circle is a mirror line. A circle has endless diameters. So it has endless mirror lines.
Shapes, compared
A regular shape has equal sides and equal angles. A square fits after a turn of 90°, 180°, 270° or 360°. A regular hexagon fits after each 60° turn.
| Shape | Smallest turn that fits | Mirror lines |
|---|---|---|
| Circle | any angle | endless |
| Equilateral triangle | 120° | 3 |
| Regular hexagon | 60° | 6 |
| Square | 90° | 4 |
| Regular pentagon | 72° | 5 |
A regular shape with n sides has n mirror lines. Its smallest turn is 360° ÷ n. For the triangle, 360 ÷ 3 = 120.
A square turned by 45° does not fit. Its corners then sit between its old corners.
Pick a shape. Slide Turn until it fits itself. Is the smallest turn 360 ÷ n?
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