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Class 6 Symmetry: cheat sheet
CBSE Mathematics. A shape is symmetrical if it folds onto itself along a line, or looks the same after a turn of less than a full turn.
Key ideas
- A line of symmetry divides a shape into two halves that are mirror images.
- A point and its mirror image are the same distance from the mirror line, on opposite sides.
- A shape has rotational symmetry if it looks the same after turning by less than a full turn.
- The order of rotational symmetry is how many times it looks the same in one full turn.
- A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
- Letters: A has one line of symmetry, H has two, and O has infinitely many.
Remember
| Angle of symmetry | 360° ÷ order of rotational symmetry |
| Regular n-gon | n lines of symmetry; order n |
| Mirror image | distance to image = 2 × distance to the line |
Watch out
- Taking a diagonal of a rectangle as a line of symmetry (it is not).
- Counting the full 360° turn as an extra order.
- Measuring only to the mirror line when asked for the distance to the image.
Worked example
A point is 29 cm from a mirror line. How far is it from its mirror image?
Working: 29 cm to the line and 29 cm on the other side
Answer: 58 cm
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