Planes of Symmetry (Edexcel IGCSE Maths)

Planes of symmetry

What is a plane 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 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

Can a 3D shape have rotational symmetry?

• 3D shapes are able to be rotated around different axes

  • Depending on which axis the shape is rotated around, 3D shapes can have rotational symmetry

• Recall that rotational symmetry is how many times the shape looks the same (congruent) when rotated through 360 degrees

  • See the example of the triangular prism where the cross-section is an equilateral triangle

Exam Hint

• 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?

Worked Example 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.

Answer:

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

Final answer: 3 planes of symmetry