What is Rotational Symmetry? [pptime time="0:01"](0:01) [/pptime]

🌟 A shape has rotational symmetry if it looks the same after being rotated by an angle less than 360°. There are 3 key parts of rotational symmetry: Centre of Rotation: The fixed point around which the shape is rotated. Angle of Rotation: The smallest angle that makes the shape look the same as before. Order of Symmetry: The number of times the shape fits onto itself in a full 360° turn. It is calculated as: $$ \text{Order of Symmetry} = \frac{360^\circ}{\text{Angle of Rotation}}$$ Example: A square has rotational symmetry because it looks the same when rotated 90 degrees. This means its angle of rotation is 90°. Since it fits onto itself 4 times in a full 360° turn (at 90°, 180°, 270°, and 360°), its order of symmetry is 4.

Rotational Symmetry of Common Figures [pptime time="1:20"](1:20) [/pptime]

Rectangle: Angle of Rotation: 180° Order of Symmetry: 2 (It fits onto itself twice in a full 360° turn at 180° and 360°). Equilateral Triangle: Angle of Rotation: 120° Order of Symmetry: 3 (It fits onto itself three times in a full 360° turn at 120°, 240°, and 360°). Regular Hexagon: Angle of Rotation: 60° Order of Symmetry: 6 (It fits onto itself six times in a full 360° turn at 60°, 120°, 180°, 240°, 300°, and 360°). Rotational symmetry helps in understanding patterns, designing objects, and solving geometric problems efficiently.

Rotational Symmetry - Definition, Formula, Shapes

🎬 Video: Understanding Rotational Symmetry

What is Rotational Symmetry? (0:01)

🌟 A shape has rotational symmetry if it looks the same after being rotated by an angle less than 360°.

There are 3 key parts of rotational symmetry:

Centre of Rotation: The fixed point around which the shape is rotated.
Angle of Rotation: The smallest angle that makes the shape look the same as before.
Order of Symmetry: The number of times the shape fits onto itself in a full 360° turn.
It is calculated as: $$ \text{Order of Symmetry} = \frac{360^\circ}{\text{Angle of Rotation}}$$

Example: A square has rotational symmetry because it looks the same when rotated 90 degrees. This means its angle of rotation is 90°. Since it fits onto itself 4 times in a full 360° turn (at 90°, 180°, 270°, and 360°), its order of symmetry is 4.

Rotational Symmetry of Common Figures (1:20)

Rectangle:
- Angle of Rotation: 180°
- Order of Symmetry: 2 (It fits onto itself twice in a full 360° turn at 180° and 360°).
Equilateral Triangle:
- Angle of Rotation: 120°
- Order of Symmetry: 3 (It fits onto itself three times in a full 360° turn at 120°, 240°, and 360°).
Regular Hexagon:
- Angle of Rotation: 60°
- Order of Symmetry: 6 (It fits onto itself six times in a full 360° turn at 60°, 120°, 180°, 240°, 300°, and 360°).