If there exists at least one axis of symmetry that divides a figure into two halves such that one- half is the mirror image of the other half, then this is called Reflection symmetry.
For example,
If a mirror is placed along the axis of symmetry of an isosceles triangle, then the reflection in the mirror will complete the image. That is the reflection of one part completes the shape.
This type of symmetry is also known as line symmetry or mirror symmetry.
What is Rotational symmetry?
When an object looks the same when it is rotated less than a complete turn, about its centre point, it is said to have Rotational symmetry.
For example,
The shape below does not have reflection symmetry.
But when it is rotated about its centre point it displays rotational symmetry.
Order of rotational symmetry
The Order of rotational symmetry of a shape is the number of times it looks exactly like the original one when rotated by 360 degrees.
For example,
The above shape when rotated by 360 degrees, looks like the original shape, twice; once when it is rotated 180 degrees and the second time when it completes a complete rotation. Hence, the shape has rotational symmetry of order 2.
Here are a few more shapes and their order of rotational symmetry.
- An oval has rotational symmetry of order
- A square has rotational symmetry of order
- An equilateral triangle has rotational symmetry of order
- A circle has rotational symmetry of order infinity. This is because no matter how the circle is rotated it will always match the original
Summary
| Reflection symmetry | There exists at least one axis of symmetry that divides a symmetrical figure into two halves such that one-half is the mirror image of the other half. |
| Rotational symmetry | An object looks the same when it is rotated less than a complete turn, about its centre point |
| Order of Rotational Symmetry | The number of times a shape looks exactly like the original one when rotated by 360 degrees |