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.
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Scalene triangle |
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Isosceles triangle |
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Equilateral triangle |
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Kite |
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Trapezium |
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Isosceles trapezium |
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Parallelogram |
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Rhombus |
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Rectangle |
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Square |
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Regular pentagon |
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Regular hexagon |
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Regular octagon |
A figure has point symmetry if it maps onto itself under a rotation of 180° (a half turn).
Summary of Transformations
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Enlargement |
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