Line symmetry
The dotted line down the middle of the letter A is called a mirror line because if you place a mirror along it, the reflection looks exactly the same as the original.
Another name for a mirror line is a line of symmetry.
This kind of symmetry can also be called reflective symmetry or reflection symmetry.
Now look what happens when you fold the letter 'A' along different examples of dotted lines.
Attempting symmetry
Image caption, The letter A is marked with fold lines.
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Only in the third example does the folded part of the shape fit exactly over the original part, so this is the only example showing a line of symmetry.
Symmetry in common shapes
If you cut out a rectangle from a piece of paper and experiment with it and a mirror, you will soon find that it has just two lines of symmetry - one lengthwise and one widthwise.
An equilateral triangle has three lines of symmetry.
Lines of symmetry
Image caption, Three lines of symmetry on an equilateral triangle.
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Rotational symmetry of a rectangle
A rectangle can be rotated about its centre by half a turn.
The result looks exactly like the original rectangle.
This is called rotational symmetry.
Image caption, Let’s count the order of rotational symmetry.
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Rotational symmetry of a regular 5-point star - Part 1
Image caption, Mark a red dot on a star as a reference point and keep an eye on it as the star rotates clockwise.
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We say that the star has rotational symmetry of order \({5}\).
If a shape only fits into itself once, it has no rotational symmetry. We also state that it has rotational symmetry of order 1.
Question
What is the order of rotational symmetry for each of the following shapes?
Answer
Test section
Question 1
How many lines of symmetry does the following shape have?
Answer
This shape only has one line of symmetry.
You can only place a mirror vertically down its centre for the shape to look exactly the same as the original.
Question 2
How many lines of symmetry does the shape below have?
Answer
This shape has three lines of symmetry.
You can place a mirror in three locations and the shape will look exactly the same as the original.
Question 3
How many lines of symmetry does the shape below have?
Answer
This shape has four lines of symmetry.
You can place a mirror in four locations and the shape will look exactly the same as the original.
Question 4
How many lines of symmetry does a rectangle have?
Answer
A rectangle has two lines of symmetry.
Question 5
How many lines of symmetry does an isosceles triangle have?
Answer
An isosceles triangle has one line of symmetry.
Question 6
How many lines of symmetry does a parallelogram have?
Answer
A parallelogram has no lines of symmetry.
Question 7
What order of rotational symmetry does the shape below have?
Answer
The order of rotational symmetry is found by counting the number of times a shape fits onto itself perfectly when turned through \({360}^\circ\).
This shape fits onto itself \({4}\) times.
Question 8
What order of rotational symmetry does the shape below have?
Answer
The degree of rotational symmetry is found by counting the number of times a shape fits onto itself perfectly when turned through \({360}^\circ\).
This shape doesn't fit perfectly until it reaches the original position so the shape has rotational symmetry of order \({1}\).
Question 9
What order of rotational symmetry does the shape below have?
Answer
The order of rotational symmetry is found by counting the number of times a shape fits onto itself perfectly when turned through \({360}^\circ\).
This shape fits onto itself \({6}\) times.
Question 10
What order of rotational symmetry does a parallelogram have?
Answer
The order of rotational symmetry is found by counting the number of times a shape fits onto itself perfectly when turned through \({360}^\circ\).
A parallelogram fits onto itself twice.
Where next?
More on Shape, space and measures
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