Skip to content
VirtusAcademy

Line Symmetry

FoundationChallengeAQAEdexcelOCR

Line Symmetry is a key geometry topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on identifying lines of symmetry, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. A line of symmetry divides a shape into mirror-image halves.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Challenge / Extension

Stretch yourself beyond the basics.

WorksheetChallenge · PDFMark SchemeChallenge · PDF

Topic overview

A shape has line symmetry if it can be folded so that one half fits exactly onto the other. The fold line is called a line of symmetry, or a mirror line.

Different shapes have different numbers. An isosceles triangle has one, a rectangle has two, a square has four, and a circle has infinitely many, since any diameter works.

The test is whether the two halves are exact mirror images. A parallelogram often catches people out: it looks symmetrical, but folding it along either diagonal does not match the halves, so it has no lines of symmetry at all.

Revision notes

Finding lines of symmetry

Imagine folding the shape along a line. If the two halves match exactly, that line is a line of symmetry.

Tracing the shape and physically folding it is a reliable check when you are unsure.

Common shapes

An isosceles triangle has \(1\), an equilateral triangle \(3\), a rectangle \(2\), a square \(4\), a rhombus \(2\) and a regular pentagon \(5\).

A regular polygon with \(n\) sides has exactly \(n\) lines of symmetry.

Shapes with none

A parallelogram has no lines of symmetry, despite appearances, because folding along a diagonal does not match the halves.

A scalene triangle also has none, since no fold produces matching halves.

Key points

  • A line of symmetry folds a shape into matching halves.
  • A square has 4 lines of symmetry.
  • A rectangle has 2.
  • An equilateral triangle has 3.
  • A regular polygon with \(n\) sides has \(n\) lines.
  • A parallelogram has none.

Worked examples

Example 1

How many lines of symmetry does a rectangle have?

Working

\[\text{Horizontal and vertical folds match}\]test each possible fold
\[2\]the diagonals do not produce matching halves

Example 2

How many lines of symmetry does a regular hexagon have?

Working

\[\text{A regular polygon has } n \text{ lines}\]use the rule for regular polygons
\[6\]a hexagon has six sides

Example 3

Explain why a parallelogram has no lines of symmetry.

Working

\[\text{Folding along a diagonal}\]test the possible fold lines
\[\text{The halves do not match}\]so there is no line of symmetry

Common mistakes

  • Counting the diagonals of a rectangle as lines of symmetry.

    Folding a rectangle along a diagonal does not match the halves, so it has only 2.

  • Assuming a parallelogram is symmetrical.

    It has rotational symmetry but no lines of symmetry.

  • Confusing line and rotational symmetry.

    Line symmetry involves folding; rotational symmetry involves turning.

  • Missing lines on a regular polygon.

    A regular n-sided polygon has exactly n lines, through vertices and edge midpoints.

Exam tips

  • Trace the shape and fold it if you are unsure.
  • Remember a regular polygon has as many lines as sides.
  • Test every possible fold, including the diagonals.
  • Keep line and rotational symmetry clearly separate.

Key terms

Line of symmetry
A fold line producing matching halves.
Mirror line
Another name for a line of symmetry.
Regular polygon
A polygon with equal sides and angles.
Scalene
A triangle with no equal sides.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.