**Symmetry**in mathematics can refer to one of two types**Line (or Plane)****symmetry**which deals with**reflections**and**mirror****images**of shapes or parts of shapes in both 2D and 3D**Rotational symmetry**which deals with how often a shape looks identical (**congruent**) when it has been rotated

**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°

- 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)

- 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

For the shape below, shade exactly 4 more squares so that the shape has rotational symmetry order 4.

For the shape below, shade exactly 4 more squares so that the shape has rotational symmetry order 4.

The shape below appears the same 4 times if rotated through 360 degrees

**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

- Each side of the line of symmetry is a

- 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

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

- 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- Use tracing paper to trace the shape and the reflection line and then flip on the line to see how the shape will reflect

- “
**Two**–**way**”**reflections**occur if the line of symmetry passes**through**the shape

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

- 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
- You should be provided with tracing paper in the exam, use this to help you

For the shape below,

(a)

Write down the number of lines of symmetry.

The only line of symmetry is shown below.

**
Answer = 1
**

**
**

(b)

Shade exactly 4 more squares so that the shape has 4 lines of symmetry.

The shape below has a horizontal, a vertical, and 2 diagonal lines of symmetry.

- A
**plane**is a flat surface that can be any 2D shape - A
**plane of symmetry**is a**plane**that splits a 3D shape into two**congruent**(identical) halves - If a 3D shape has a plane of symmetry, it has reflection symmetry
- The two congruent halves are identical, mirror images of each other

- All
**prisms**have at least one plane of symmetry**Cubes**have 9 planes of symmetry**Cuboids**have 3 planes of symmetry**Cylinders**have an infinite number of planes of symmetry- The number of planes of symmetry in other prisms will be equal to the number of lines of symmetry in its cross-section plus 1

**Pyramids**can have planes of symmetry too- The number of planes of symmetry in other pyramids will be equal to the number of lines of symmetry in its 2D base
- If the base of the pyramid is a
**regular polygon**of*n*sides, it will have*n*planes of symmetry

If you’re unsure in the exam, consider the properties of the 3D shape.

- Is it a
**prism**or a**pyramid**? - How many
**lines of symmetry**are there in the**2D**faces or cross-section?

The diagram below shows a cuboid of length 8 cm, width 5 cm and height 11 cm.

Write down the number of planes of symmetry of this cuboid.

A plane of symmetry is where a shape can be “sliced” such that it is symmetrical.

A cuboid with three different pairs of opposite rectangles has 3 planes of symmetry.

**
3 planes of symmetry
**

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