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- 2D Shapes
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- Lines of symmetry
Symmetry is all around us. If you turn an object round will it look the same? Let’s see an example:
You can see the above shape when rotated by 90° twice, gives the same shape. So this shape has rotational symmetry. Let us now see what exactly is rotational symmetry,
1. What is rotational symmetry?
A shape is said to have rotational symmetry which when rotated about its center, looks the same in more than one position and the number of such positions is called the order of rotational symmetry.
Look at the shape below.
This shape looks the same when rotated around the center in three different positions. So this shape has 3 orders of rotational symmetry.
Examples of shapes and order of rotational symmetry:
1.1 Rotational symmetry of simple Quadrilaterals
1.2 Shapes with no lines of symmetry
Can you think of some shapes which have no rotational symmetry? Most of the irregular
Shapes do not have rotational symmetry.
The order of such shapes that don't have a rotational symmetry is one.
Let's take a look at a few of these shapes.
2. Rotational Symmetry for Regular Polygons
Regular polygons:- Regular polygons are shapes with all sides of equal length.
All the regular polygons have rotational symmetry. The order of
rotational symmetry for a regular polygon is equal to its number of
sides.
Let us look at rotational symmetry of some regular polygons.
3. Solved Examples
Example 1 : The figure shows an equilateral triangle divided into smaller equilateral triangles. What is the lowest number of triangles that must be shaded to produce a figure that has 3 orders of rotational symmetry?
Solution:
So we need to shade 2 triangles to have rotational symmetry of order 3.
Example 2: Arrange the following shapes in the increasing order of rotational symmetry.
- Square
- Regular heptagon
- Regular decagon
- Equilateral Triangle
- Regular octagon
Solution: Regular polygons of n sides have n orders of rotational symmetry.
Square has 4 orders of rotational symmetry.
A regular heptagon has 7 sides, so it has 7 orders of rotational symmetry.
A regular decagon has 10 sides, so it has 10 orders of rotational symmetry.
An equilateral triangle has 3 orders of rotational symmetry.
A regular octagon has 8 sides, so it has 8 orders of rotational symmetry.
Increasing order : D < A < B < E < C
