There are two types of symmetry: line symmetry, which involves reflection, and rotational symmetry, which involves rotation. The total order of symmetry of a shape is the sum of the number of lines of symmetry and the order of rotational symmetry of the figure.
Line Symmetry
A figure has a line of symmetry if it maps onto itself under reflection in the line.
e.g.
- A rectangle has 2 axes of symmetry. (m and n are axes of symmetry.)
- A regular hexagon has 6 axes of symmetry.
- A circle has an infinite number of axes of symmetry.
Rotational Symmetry
A figure has rotational symmetry if it maps onto itself under rotation about a point at its centre.
The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°.
e.g.
- A rectangle has order of rotational symmetry of 2.
180° and 360° rotations will map it onto itself.
- A regular hexagon has order of rotational symmetry of 6.
- A scalene triangle, with no equal sides or angles has
order of rotational symmetry of 1.
- All figures have an order of rotational symmetry of at least 1.
Total Order of Symmetry
The total order of symmetry = number of axes of symmetry + order of rotational symmetry.
The table shows the symmetry properties of some common shapes.
Scalene triangle |
|||
Isosceles triangle |
|||
Equilateral triangle |
|||
Kite |
|||
Trapezium |
|||
Isosceles trapezium |
|||
Parallelogram |
|||
Rhombus |
|||
Rectangle |
|||
Square |
|||
Regular pentagon |
|||
Regular hexagon |
|||
Regular octagon |
A figure has point symmetry if it maps onto itself under a rotation of 180° (a half turn).
Summary of Transformations
Enlargement |
|||