Symmetry

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Recognise line symmetry and order of rotational symmetry in two-dimensional shapes
  2. Understand how the properties of triangles, quadrilaterals, and polygons relate to their symmetries
  3. Recognise symmetry properties of three-dimensional shapes including prisms, cylinders, pyramids, and cones
  4. Identify planes and axes of symmetry in three-dimensional shapes

What is Symmetry?

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Symmetry is when a shape looks balanced or the same when you move it in a certain way. There are two main types of symmetry you need to understand: line symmetry and rotational symmetry.

Line Symmetry

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What is Line Symmetry?

A shape has line symmetry (also called reflective symmetry or mirror symmetry) when you can draw a line through it that divides the shape into two identical halves. Each half is a mirror image of the other.

This line is called a line of symmetry or mirror line.

The Folding Test

Here's an easy way to check if a line is a line of symmetry: imagine folding the shape along the line. If both halves fit exactly on top of each other, then it's a line of symmetry.

Examples of Line Symmetry

Rectangle: A rectangle has 2 lines of symmetry. One line runs horizontally through the middle, and the other runs vertically through the middle. Note that the diagonals are NOT lines of symmetry because if you fold along a diagonal, the two halves don't match up perfectly.

Square: A square has 4 lines of symmetry. It has a horizontal line, a vertical line, and two diagonal lines (connecting opposite corners).

Isosceles Triangle: An isosceles triangle has 1 line of symmetry that runs vertically from the top point down to the middle of the base.

Equilateral Triangle: An equilateral triangle has 3 lines of symmetry, each running from one corner to the middle of the opposite side.

How to Draw Lines of Symmetry

  1. Look at the shape from different angles (you can turn your paper)
  2. Try to imagine folding the shape in different ways
  3. Draw a dashed line where the fold would be
  4. Check that both sides are mirror images

Completing Symmetrical Shapes

Sometimes in exams, you'll be given half a shape and a line of symmetry, and you need to complete the other half. Here's how:

  1. Look at each point or corner on one side of the line
  2. Measure how far it is from the line of symmetry
  3. Draw the matching point the same distance away on the other side
  4. Connect the points to complete the shape
  5. Use tracing paper if allowed - trace one half, flip the paper along the line, and draw the reflection

Important: Be especially careful with diagonal lines of symmetry. They can be tricky!

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