Symmetry (Including Reflection and Rotation)
ICSE Class 7 · Mathematics · Chapter 17
What this chapter covers
- What symmetry means
- Reflection symmetry
- Reflection as an operation
- Rotation: turning a figure about a point
- Rotational symmetry: centre, angle and order
- Rotation through 90, 120 and 180 degrees
- Figures with both kinds of symmetry
- Symmetry around you
Key points
- Symmetry is an exact match between parts of a figure under folding, reflecting or turning.
- A line of symmetry divides a figure into two halves that match exactly when folded.
- A regular polygon with n sides has n lines of symmetry; a circle has infinitely many.
- In a reflection, each point and its image are equally far from the mirror line, on a perpendicular to it.
- A rotation turns a figure about a fixed centre through an angle, clockwise or anticlockwise.
- A figure has rotational symmetry if it fits onto itself after a turn of less than 360°.
- The order of rotational symmetry is the number of fits in one full turn; order = 360° ÷ angle.
- Angle 180° gives order 2 (rectangle, parallelogram, S, Z); 120° gives order 3 (equilateral triangle); 90° gives order 4 (square).
- Order 1 means no rotational symmetry.
- Squares, rectangles, equilateral triangles and circles have both kinds of symmetry; a parallelogram has rotational symmetry only; a kite has line symmetry only.