CIE IGCSE Maths

Revision Notes

4.3.1 Symmetry

What is symmetry?

  • Symmetry in mathematics can refer to one of two types:
    • Line symmetry which deals with reflections and mirror images of shapes or parts of shapes
    • Rotational symmetry which deals with how often a shape looks identical (congruent) when it has been rotated

 

Symm Notes fig1, downloadable IGCSE & GCSE Maths revision notes

What is line symmetry?

  • Line symmetry refers to shapes that can have mirror lines added to them
    • Each side of the line of symmetry is a reflection of the other side
  • Lines of symmetry can be thought of as a folding line too
    • Folding a shape along a line of symmetry results in the two parts sitting exactly on top of each other

 

Symm Notes fig2a, downloadable IGCSE & GCSE Maths revision notes

  • It can help to look at shapes from different angles – turn the page to do this

 

Symm Notes fig2b, downloadable IGCSE & GCSE Maths revision notes

  • Some questions will provide a shape and a line of symmetry
    • In these cases you need to complete the shape
  • Be careful with diagonal lines of symmetry!
  • Twowayreflections occur if the line of symmetry passes through the shape

 

Symm Notes fig2c (1), downloadable IGCSE & GCSE Maths revision notes Symm Notes fig2c (2), downloadable IGCSE & GCSE Maths revision notes

What is (the order of) rotational symmetry?

  • Rotational symmetry refers to the number of times a shape looks the same as it is rotated 360° about its centre
  • This number is called the order of rotational symmetry
  • Tracing paper can help work out the order of rotational symmetry
    • Draw an arrow on the tracing paper so you can easily tell when you have turned it through 360°

 

Symm Notes fig3a (1), downloadable IGCSE & GCSE Maths revision notes

Symm Notes fig3a (2), downloadable IGCSE & GCSE Maths revision notes

Symm Notes fig3b, downloadable IGCSE & GCSE Maths revision notes

  • Notice that returning to the original shape contributes 1 to the order
    • This means a shape can never have order 0
    • A shape with rotational symmetry order 1 may be described as not having any rotational symmetry
      (The only time it looks the same is when you get back to the start)

How do I solve problems involving symmetry?

  • Symmetry can be used to help solve missing length and angle problems

 

Symm Notes fig4 (1), downloadable IGCSE & GCSE Maths revision notes Symm Notes fig4 (2), downloadable IGCSE & GCSE Maths revision notes

Exam Tip

It may help to draw a diagram and add lines of symmetry to it – or add to a diagram if one is given in a question.

Tracing paper may help for rotational symmetry. One trick is to draw an arrow facing upwards so that when you rotate the tracing paper you know when it is back to its original position.

Worked Example

Symm Example qu, downloadable IGCSE & GCSE Maths revision notes Symm Example sol, downloadable IGCSE & GCSE Maths revision notes

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