Symmetry and the properties of quadrilaterals

Shapes are recognised by their symmetry, sides, angles and diagonals. Knowing these properties is the key to many angle problems.

GCSE · 1MA1 · G1, G4
International GCSE · 4MA1 · 4.2, 4.3
About 14 minutes

Practise this lesson free (6 questions)

Two kinds of symmetry

Line symmetry: a mirror line folds the shape onto itself.
Rotational symmetry: the order is how many times the shape looks the same in one full turn.
A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.

Quadrilaterals

Shape	Sides	Angles	Diagonals	Lines	Order
Square	4 equal, 2 pairs parallel	all 90°	equal, bisect at 90°	4	4
Rectangle	2 pairs equal and parallel	all 90°	equal, bisect each other	2	2
Rhombus	4 equal, 2 pairs parallel	opposite equal	bisect at 90°	2	2
Parallelogram	2 pairs equal and parallel	opposite equal	bisect each other	0	2
Kite	2 pairs of equal adjacent sides	one pair equal	cross at 90°	1	1
Trapezium	1 pair parallel			0 (isosceles: 1)	1

Notation

Label corners with capital letters going round the shape: ABCD.
Angle ABC (or ∠ABC) is the angle at B between BA and BC.
Side AB is opposite angle C in triangle ABC, and is often called c.
Equal sides are shown by dashes; parallel sides by arrows.

Worked example

How many lines of symmetry and what order of rotational symmetry does a regular hexagon have?

A regular polygon with n sides has n lines of symmetry.
Its rotational symmetry also has order n.

Answer: 6 lines, order 6

Key idea

Line symmetry: mirror lines. Rotational symmetry: how many times it fits in a full turn. Learn the sides, angles and diagonals of the six special quadrilaterals.

Common mistakes

Not “Kite”. Only one diagonal of a kite is bisected.

Quick check

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Extra practice

2 more questions

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How many lines of symmetry does a square have?
Show the answer
Answer: 4
Two through the middles of the sides and two diagonals: 4.
What is the order of rotational symmetry of an equilateral triangle?
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Answer: 3
It looks the same 3 times (every 120°) in a full turn, so the order is 3.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.