Sec 1 · G3 (Express)

Triangles, quadrilaterals and polygons

Practise triangles, quadrilaterals and polygons with step-by-step help. Free account.

1. Triangles

Triangle	Property	Reason to write
any	angles add up to $180^\circ$	$\angle$ sum of $\triangle$
isosceles	two equal sides; the base angles opposite them are equal	base $\angle$ s of isos. $\triangle$
equilateral	three equal sides; each angle is $60^\circ$	equil. $\triangle$
right-angled	one angle is $90^\circ$
exterior angle	equals the sum of the two interior opposite angles	ext. $\angle$ of $\triangle$

Left: triangle ABC with angles 52° at A and 67° at C; AB extended past B makes an exterior angle of 119°, which is 52° + 67°. Right: a hexagon with its sides extended, showing the exterior angle at each vertex.

Isosceles: apex 44°, find each base angle x

\displaystyle 2x + 44 = 180

e.g.

\displaystyle 2x + 44 = 180

\displaystyle 2x = 136

\displaystyle x = 68

Exterior angle at B

\displaystyle 52^\circ + 67^\circ

e.g.

\displaystyle 52 + 67

\displaystyle = 119

📖 Worked example

In triangle $ABC$ , $AB = AC$ . Find $x$ .

Step 1 of 2

Use AB = AC: find ∠ACB and give the reason

\angle ACB = 62^\circ

(base ∠s of isos. △)

📖 Worked example

In the diagram, $BC$ is produced to $D$ . Find $x$ .

Step 1 of 2

Which angle fact gives x?

112^\circ = 46^\circ + x^\circ

(ext. ∠ of △)

📖 Worked example

The diagram shows triangle $XYZ$ . Is triangle $XYZ$ isosceles? Choose the answer with its reason.

Step 1 of 4

Write an equation in x

(x + 20)^\circ + (2x + 92)^\circ + (2x + 8)^\circ = 180^\circ

(∠ sum of △)

Practise this →

2. Quadrilaterals

Quadrilateral	Sides	Angles	Diagonals
parallelogram	opposite sides parallel and equal	opposite angles equal	bisect each other
rectangle	opposite sides parallel and equal	all $90^\circ$	equal, bisect each other
rhombus	all equal	opposite angles equal	bisect each other at $90^\circ$
square	all equal	all $90^\circ$	equal, bisect each other at $90^\circ$
trapezium	one pair parallel
isosceles trapezium	one pair parallel; the other two sides equal	base angles equal	equal
kite	two pairs of equal adjacent sides	one pair equal	cross at $90^\circ$ ; one bisects the other

📖 Worked example

$ABCD$ is a parallelogram. Find $x$ .

Step 1 of 2

Which angle fact gives x?

x^\circ + 113^\circ = 180^\circ

(int. ∠s,

AB \parallel DC

)

Angles in a ratio	Share	Example
$\angle A : \angle B : \angle C : \angle D$	$360^\circ$	$3 : 4 : 5 : 6$ : $18$ units $\rightarrow 360^\circ$ , $1$ unit $\rightarrow 20^\circ$
parallelogram, $\angle A : \angle B$	$180^\circ$ (int. $\angle$ s)	$2 : 3$ : $1$ unit $\rightarrow 36^\circ$

📖 Worked example

In the quadrilateral $ABCD$ , $\angle A : \angle B : \angle C : \angle D = 3 : 4 : 5 : 6$ . Find $x$ .

Step 1 of 2

The four angles add up to 360°: share 360° in the ratio

Total units

= 3 + 4 + 5 + 6

= 18

1

unit

\rightarrow \dfrac{360^\circ}{18} = 20^\circ

(∠ sum of quad.)

📖 Worked example

$ABCD$ is a square and $AC$ is a diagonal. $E$ is a point inside the square such that $DE = DC$ . Find $x$ .

Step 1 of 3

∠ADC of the square is 90°: find ∠EDC

\angle EDC = 90^\circ - 24^\circ

\phantom{\angle EDC} = 66^\circ

Practise this →

3. Polygons

$n$ sides	Formula	Example: hexagon, $n = 6$
sum of interior angles	$(n - 2) \times 180^\circ$	$720^\circ$
sum of exterior angles	$360^\circ$	$360^\circ$
each exterior angle (regular)	$\dfrac{360^\circ}{n}$	$60^\circ$
each interior angle (regular)	$180^\circ - \text{exterior angle}$	$120^\circ$

Number of sides of a regular polygon with interior angle 156°

\displaystyle \text{exterior angle} = 180^\circ - 156^\circ

e.g.

\displaystyle n = \dfrac{360}{180 - 156}

\displaystyle n = 15

📖 Worked example

The diagram shows a regular nonagon. Find $x$ .

Step 1 of 2

Sum of the interior angles of a nonagon

(9 - 2) \times 180^\circ = 1260^\circ

📖 Worked example

Each interior angle of a regular polygon is $3$ times each of its exterior angles. Find the number of sides of the polygon.

Step 1 of 3

An interior angle and its exterior angle make a straight line: together 180°

3 + 1 = 4

units

\rightarrow 180^\circ

1

unit

\rightarrow \dfrac{180}{4} = 45^\circ

📖 Worked example

In the diagram, a square, a regular pentagon and a regular polygon with $n$ sides fit together round the point $O$ , with no gaps. Find $n$ .

Step 1 of 3

Each interior angle of the two known polygons: (n − 2) × 180° ÷ n

Square:

90^\circ

Regular pentagon:

108^\circ

📖 Worked example

A polygon has $n$ sides. 3 of its interior angles are $100^\circ$ , $120^\circ$ and $140^\circ$ . Each of the other interior angles is $165^\circ$ . Find $n$ .

Step 1 of 3

Work with exterior angles (180° − each interior angle): they add up to 360°

Exterior angles of the given ones:

180^\circ - 100^\circ = 80^\circ

180^\circ - 120^\circ = 60^\circ

180^\circ - 140^\circ = 40^\circ

Their sum

= 180^\circ

📖 Worked example

The diagram shows a regular hexagon $ABCD\ldots$ with the diagonal $AC$ . Find $x$ .

Step 1 of 2

Each interior angle of the regular polygon

\angle ABC = \dfrac{(6 - 2) \times 180}{6}

\phantom{\angle ABC} = 120^\circ

📖 Worked example

The diagram shows a regular pentagon $ABCDE$ and a square $CDQP$ drawn inside it on the side $CD$ . $B$ is joined to $P$ . Find $x$ .

Step 1 of 4

Each interior angle of the regular pentagon

\angle BCD = \dfrac{(5 - 2) \times 180^\circ}{5}

\phantom{\angle BCD} = 108^\circ

📖 Worked example

A polygon has one reflex interior angle of $205^\circ$ . Each of its other interior angles is $145^\circ$ . Find the number of sides of the polygon.

Step 1 of 3

The interior angles of an n-sided polygon add up to (n − 2) × 180°

(n - 2) \times 180 = 205 + (n - 1) \times 145

(∠ sum of polygon)

Practise this →

4. Special quadrilaterals

The seven special quadrilaterals with their marks and dashed diagonals: a square (four equal sides, four right angles, diagonals at right angles); a rectangle (opposite sides equal, four right angles); a rhombus (four equal sides, diagonals at right angles); a parallelogram (both pairs of opposite sides parallel); a kite (two pairs of equal sides next to each other, diagonals at right angles); a trapezium (one pair of parallel sides); an isosceles trapezium (one pair of parallel sides, the other two sides equal, base angles both 64°).

Property	square	rectangle	rhombus	parallelogram	kite	trapezium	isosceles trapezium
all sides equal	✓	✗	✓	✗	✗	✗	✗
both pairs of opposite sides parallel	✓	✓	✓	✓	✗	✗	✗
only one pair of parallel sides	✗	✗	✗	✗	✗	✓	✓
all angles $90^\circ$	✓	✓	✗	✗	✗	✗	✗
opposite angles equal	✓	✓	✓	✓	✗	✗	✗
diagonals bisect each other	✓	✓	✓	✓	✗	✗	✗
diagonals equal	✓	✓	✗	✗	✗	✗	✓
diagonals cross at $90^\circ$	✓	✗	✓	✗	✓	✗	✗
diagonals bisect the angles	✓	✗	✓	✗	✗	✗	✗

📖 Worked example

The marks on the diagram show what is known about quadrilateral $ABCD$ . Write down the most special name of $ABCD$ .

Step 1 of 4

Equal sides (the ticks)

Equal sides: all four.

📖 Worked example

$ABCD$ is a rhombus. Its diagonals meet at $O$ . $AC = 12$ cm and $BD = 16$ cm. Find $AB$ .

Step 1 of 2

The diagonals of a rhombus bisect each other at right angles

OA = 6

cm,

OB = 8

\angle AOB = 90^\circ

📖 Worked example

$ABCD$ is a rectangle. Its diagonals meet at $O$ , and $\angle OAB = 28^\circ$ . Find $x$ .

Step 1 of 2

Find ∠OBA and give the reason

\angle OBA = 28^\circ

(base ∠s of isos. △)

The angles show	Sides not all equal	Four equal sides
all four angles $90^\circ$	rectangle	square
both pairs of opposite angles equal	parallelogram	rhombus
only $\angle A + \angle D = 180^\circ$ ( $AB \parallel DC$ )	trapezium

📖 Worked example

The diagram shows a quadrilateral $ABCD$ . By finding $x$ , name the special quadrilateral $ABCD$ .

Step 1 of 5

Write an equation in x

3x^\circ + (2x + 30)^\circ + 90^\circ + (x + 60)^\circ = 360^\circ

(∠ sum of quad.)

Practise this →

5. Constructing triangles and quadrilaterals

Three sides (SSS), AB = 7 cm, AC = 5 cm, BC = 6 cm: 1. draw AB = 7 cm; 2. an arc of radius 5 cm about A; 3. an arc of radius 6 cm about B cuts it at C; join AC and BC.

Two sides and the angle between them (SAS), AB = 7 cm, angle ABC = 50°, BC = 5 cm: 1. draw AB; 2. a protractor at B, 50°, and a ray; 3. an arc of radius 5 cm about B cuts the ray at C; join AC.

Two angles and the side between them (ASA), AB = 7 cm, angle BAC = 50°, angle ABC = 60°: 1. draw AB; 2. a ray at 50° from A; 3. a ray at 60° from B; the rays cross at C.

Given	Tools	Fixes one triangle?
three sides (SSS)	ruler, compasses	yes, if the two shorter sides add up to more than the longest
two sides and the angle between (SAS)	ruler, protractor, compasses	yes
two angles and the side between (ASA)	ruler, protractor	yes, if the two angles add up to less than $180^\circ$
three angles		no: any size

📖 Worked example

Jun Jie is constructing triangle $ABC$ with $AB = 7$ cm, $AC = 5$ cm and $BC = 6$ cm. The diagram shows the construction so far. Which of the following is the next step?

Step 1 of 2

How many steps are done?

Done: draw AB, arc about A.

📖 Worked example

Construct triangle $ABC$ with $AB = 6$ cm, $\angle ABC = 115^\circ$ and $BC = 5$ cm. Measure the length of $AC$ , to the nearest $0.1$ cm.

Step 1 of 4

Draw the base AB with a ruler

Draw

AB = 6

cm.

📖 Worked example

Construct quadrilateral $ABCD$ with $AB = 4$ cm, $BC = 6$ cm, $CD = 5$ cm, $DA = 6$ cm and the diagonal $AC = 7$ cm. Measure the length of the diagonal $BD$ , to the nearest $0.1$ cm.

Step 1 of 4

Start with the diagonal: it splits ABCD into two triangles

Draw

AC = 7

cm.

Practise this →

6. Line symmetry

Lines of symmetry dashed: a square has 4, a rectangle 2, an equilateral triangle 3, a rhombus 2 (its diagonals), a parallelogram 0, a kite 1, an isosceles trapezium 1 and a regular hexagon 6.

Word	Meaning
line of symmetry	a fold line: the two halves match exactly
regular polygon, $n$ sides	$n$ lines of symmetry

📖 Worked example

The diagram shows a kite. State whether the dashed line is a line of symmetry of the shape.

Step 1 of 2

Imagine folding the shape along the dashed line

Each corner on one side must land exactly on a corner on the other side, and each side on a side.

📖 Worked example

The diagram shows a rectangle. Write down the number of lines of symmetry of the shape.

Step 1 of 2

Look for every fold line that makes the two halves match

Lines of symmetry: the two lines joining the middles of opposite sides (not the diagonals).

Practise this →

7. Rotational symmetry

Each shape turned about its centre until a marked corner lands on the next corner: an equilateral triangle after 120° (order 3), a square after 90° (order 4), a parallelogram after 180° (order 2); a kite fits only after a full turn (order 1).

Order: how many times it fits in one full turn

\displaystyle \text{angle of rotation} = \dfrac{360^\circ}{\text{order}}

e.g.

\displaystyle \dfrac{360^\circ}{4}

\displaystyle = 90^\circ

a square: order $4$

Shape	Lines of symmetry	Order	Angle of rotation
square	$4$	$4$	$90^\circ$
rectangle	$2$	$2$	$180^\circ$
equilateral triangle	$3$	$3$	$120^\circ$
rhombus	$2$	$2$	$180^\circ$
parallelogram	$0$	$2$	$180^\circ$
kite	$1$	$1$
regular hexagon	$6$	$6$	$60^\circ$

📖 Worked example

The diagram shows a propeller shape. Write down its order of rotational symmetry.

Step 1 of 1

Turn the shape about its centre: in one full turn, how many times does it look exactly the same?

It looks the same every third of a turn.

\text{Order} = 3

📖 Worked example

The diagram shows an equilateral triangle. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

Step 1 of 2

Turn the shape about its centre: in one full turn, how many times does it look exactly the same?

It looks the same every third of a turn.

\text{Order} = 3

Practise this →

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Sec 1 · G3 (Express)

Triangles, quadrilaterals and polygons

Practise triangles, quadrilaterals and polygons with step-by-step help. Free account.

Start free Worksheet (PDF)

1. Triangles

Triangle	Property	Reason to write
any	angles add up to $180^\circ$	$\angle$ sum of $\triangle$
isosceles	two equal sides; the base angles opposite them are equal	base $\angle$ s of isos. $\triangle$
equilateral	three equal sides; each angle is $60^\circ$	equil. $\triangle$
right-angled	one angle is $90^\circ$
exterior angle	equals the sum of the two interior opposite angles	ext. $\angle$ of $\triangle$

Isosceles: apex 44°, find each base angle x

\displaystyle 2x + 44 = 180

e.g.

\displaystyle 2x + 44 = 180

\displaystyle 2x = 136

\displaystyle x = 68

Exterior angle at B

\displaystyle 52^\circ + 67^\circ

e.g.

\displaystyle 52 + 67

\displaystyle = 119

📖 Worked example

In triangle $ABC$ , $AB = AC$ . Find $x$ .

Step 1 of 2

Use AB = AC: find ∠ACB and give the reason

\angle ACB = 62^\circ

(base ∠s of isos. △)

📖 Worked example

In the diagram, $BC$ is produced to $D$ . Find $x$ .

Step 1 of 2

Which angle fact gives x?

112^\circ = 46^\circ + x^\circ

(ext. ∠ of △)

📖 Worked example

The diagram shows triangle $XYZ$ . Is triangle $XYZ$ isosceles? Choose the answer with its reason.

Step 1 of 4

Write an equation in x

(x + 20)^\circ + (2x + 92)^\circ + (2x + 8)^\circ = 180^\circ

(∠ sum of △)

Practise this →

2. Quadrilaterals

Quadrilateral	Sides	Angles	Diagonals
parallelogram	opposite sides parallel and equal	opposite angles equal	bisect each other
rectangle	opposite sides parallel and equal	all $90^\circ$	equal, bisect each other
rhombus	all equal	opposite angles equal	bisect each other at $90^\circ$
square	all equal	all $90^\circ$	equal, bisect each other at $90^\circ$
trapezium	one pair parallel
isosceles trapezium	one pair parallel; the other two sides equal	base angles equal	equal
kite	two pairs of equal adjacent sides	one pair equal	cross at $90^\circ$ ; one bisects the other

📖 Worked example

$ABCD$ is a parallelogram. Find $x$ .

Step 1 of 2

Which angle fact gives x?

x^\circ + 113^\circ = 180^\circ

(int. ∠s,

AB \parallel DC

)

Angles in a ratio	Share	Example
$\angle A : \angle B : \angle C : \angle D$	$360^\circ$	$3 : 4 : 5 : 6$ : $18$ units $\rightarrow 360^\circ$ , $1$ unit $\rightarrow 20^\circ$
parallelogram, $\angle A : \angle B$	$180^\circ$ (int. $\angle$ s)	$2 : 3$ : $1$ unit $\rightarrow 36^\circ$

📖 Worked example

In the quadrilateral $ABCD$ , $\angle A : \angle B : \angle C : \angle D = 3 : 4 : 5 : 6$ . Find $x$ .

Step 1 of 2

The four angles add up to 360°: share 360° in the ratio

Total units

= 3 + 4 + 5 + 6

= 18

1

unit

\rightarrow \dfrac{360^\circ}{18} = 20^\circ

(∠ sum of quad.)

📖 Worked example

$ABCD$ is a square and $AC$ is a diagonal. $E$ is a point inside the square such that $DE = DC$ . Find $x$ .

Step 1 of 3

∠ADC of the square is 90°: find ∠EDC

\angle EDC = 90^\circ - 24^\circ

\phantom{\angle EDC} = 66^\circ

Practise this →

3. Polygons

$n$ sides	Formula	Example: hexagon, $n = 6$
sum of interior angles	$(n - 2) \times 180^\circ$	$720^\circ$
sum of exterior angles	$360^\circ$	$360^\circ$
each exterior angle (regular)	$\dfrac{360^\circ}{n}$	$60^\circ$
each interior angle (regular)	$180^\circ - \text{exterior angle}$	$120^\circ$

Number of sides of a regular polygon with interior angle 156°

\displaystyle \text{exterior angle} = 180^\circ - 156^\circ

e.g.

\displaystyle n = \dfrac{360}{180 - 156}

\displaystyle n = 15

📖 Worked example

The diagram shows a regular nonagon. Find $x$ .

Step 1 of 2

Sum of the interior angles of a nonagon

(9 - 2) \times 180^\circ = 1260^\circ

📖 Worked example

Each interior angle of a regular polygon is $3$ times each of its exterior angles. Find the number of sides of the polygon.

Step 1 of 3

An interior angle and its exterior angle make a straight line: together 180°

3 + 1 = 4

units

\rightarrow 180^\circ

1

unit

\rightarrow \dfrac{180}{4} = 45^\circ

📖 Worked example

In the diagram, a square, a regular pentagon and a regular polygon with $n$ sides fit together round the point $O$ , with no gaps. Find $n$ .

Step 1 of 3

Each interior angle of the two known polygons: (n − 2) × 180° ÷ n

Square:

90^\circ

Regular pentagon:

108^\circ

📖 Worked example

A polygon has $n$ sides. 3 of its interior angles are $100^\circ$ , $120^\circ$ and $140^\circ$ . Each of the other interior angles is $165^\circ$ . Find $n$ .

Step 1 of 3

Work with exterior angles (180° − each interior angle): they add up to 360°

Exterior angles of the given ones:

180^\circ - 100^\circ = 80^\circ

180^\circ - 120^\circ = 60^\circ

180^\circ - 140^\circ = 40^\circ

Their sum

= 180^\circ

📖 Worked example

The diagram shows a regular hexagon $ABCD\ldots$ with the diagonal $AC$ . Find $x$ .

Step 1 of 2

Each interior angle of the regular polygon

\angle ABC = \dfrac{(6 - 2) \times 180}{6}

\phantom{\angle ABC} = 120^\circ

📖 Worked example

The diagram shows a regular pentagon $ABCDE$ and a square $CDQP$ drawn inside it on the side $CD$ . $B$ is joined to $P$ . Find $x$ .

Step 1 of 4

Each interior angle of the regular pentagon

\angle BCD = \dfrac{(5 - 2) \times 180^\circ}{5}

\phantom{\angle BCD} = 108^\circ

📖 Worked example

A polygon has one reflex interior angle of $205^\circ$ . Each of its other interior angles is $145^\circ$ . Find the number of sides of the polygon.

Step 1 of 3

The interior angles of an n-sided polygon add up to (n − 2) × 180°

(n - 2) \times 180 = 205 + (n - 1) \times 145

(∠ sum of polygon)

Practise this →

4. Special quadrilaterals

Property	square	rectangle	rhombus	parallelogram	kite	trapezium	isosceles trapezium
all sides equal	✓	✗	✓	✗	✗	✗	✗
both pairs of opposite sides parallel	✓	✓	✓	✓	✗	✗	✗
only one pair of parallel sides	✗	✗	✗	✗	✗	✓	✓
all angles $90^\circ$	✓	✓	✗	✗	✗	✗	✗
opposite angles equal	✓	✓	✓	✓	✗	✗	✗
diagonals bisect each other	✓	✓	✓	✓	✗	✗	✗
diagonals equal	✓	✓	✗	✗	✗	✗	✓
diagonals cross at $90^\circ$	✓	✗	✓	✗	✓	✗	✗
diagonals bisect the angles	✓	✗	✓	✗	✗	✗	✗

📖 Worked example

The marks on the diagram show what is known about quadrilateral $ABCD$ . Write down the most special name of $ABCD$ .

Step 1 of 4

Equal sides (the ticks)

Equal sides: all four.

📖 Worked example

$ABCD$ is a rhombus. Its diagonals meet at $O$ . $AC = 12$ cm and $BD = 16$ cm. Find $AB$ .

Step 1 of 2

The diagonals of a rhombus bisect each other at right angles

OA = 6

cm,

OB = 8

\angle AOB = 90^\circ

📖 Worked example

$ABCD$ is a rectangle. Its diagonals meet at $O$ , and $\angle OAB = 28^\circ$ . Find $x$ .

Step 1 of 2

Find ∠OBA and give the reason

\angle OBA = 28^\circ

(base ∠s of isos. △)

The angles show	Sides not all equal	Four equal sides
all four angles $90^\circ$	rectangle	square
both pairs of opposite angles equal	parallelogram	rhombus
only $\angle A + \angle D = 180^\circ$ ( $AB \parallel DC$ )	trapezium

📖 Worked example

The diagram shows a quadrilateral $ABCD$ . By finding $x$ , name the special quadrilateral $ABCD$ .

Step 1 of 5

Write an equation in x

3x^\circ + (2x + 30)^\circ + 90^\circ + (x + 60)^\circ = 360^\circ

(∠ sum of quad.)

Practise this →

5. Constructing triangles and quadrilaterals

Given	Tools	Fixes one triangle?
three sides (SSS)	ruler, compasses	yes, if the two shorter sides add up to more than the longest
two sides and the angle between (SAS)	ruler, protractor, compasses	yes
two angles and the side between (ASA)	ruler, protractor	yes, if the two angles add up to less than $180^\circ$
three angles		no: any size

📖 Worked example

Jun Jie is constructing triangle $ABC$ with $AB = 7$ cm, $AC = 5$ cm and $BC = 6$ cm. The diagram shows the construction so far. Which of the following is the next step?

Step 1 of 2

How many steps are done?

Done: draw AB, arc about A.

📖 Worked example

Construct triangle $ABC$ with $AB = 6$ cm, $\angle ABC = 115^\circ$ and $BC = 5$ cm. Measure the length of $AC$ , to the nearest $0.1$ cm.

Step 1 of 4

Draw the base AB with a ruler

Draw

AB = 6

cm.

📖 Worked example

Construct quadrilateral $ABCD$ with $AB = 4$ cm, $BC = 6$ cm, $CD = 5$ cm, $DA = 6$ cm and the diagonal $AC = 7$ cm. Measure the length of the diagonal $BD$ , to the nearest $0.1$ cm.

Step 1 of 4

Start with the diagonal: it splits ABCD into two triangles

Draw

AC = 7

cm.

Practise this →

6. Line symmetry

Word	Meaning
line of symmetry	a fold line: the two halves match exactly
regular polygon, $n$ sides	$n$ lines of symmetry

📖 Worked example

The diagram shows a kite. State whether the dashed line is a line of symmetry of the shape.

Step 1 of 2

Imagine folding the shape along the dashed line

Each corner on one side must land exactly on a corner on the other side, and each side on a side.

📖 Worked example

The diagram shows a rectangle. Write down the number of lines of symmetry of the shape.

Step 1 of 2

Look for every fold line that makes the two halves match

Lines of symmetry: the two lines joining the middles of opposite sides (not the diagonals).

Practise this →

7. Rotational symmetry

Order: how many times it fits in one full turn

\displaystyle \text{angle of rotation} = \dfrac{360^\circ}{\text{order}}

e.g.

\displaystyle \dfrac{360^\circ}{4}

\displaystyle = 90^\circ

a square: order $4$

Shape	Lines of symmetry	Order	Angle of rotation
square	$4$	$4$	$90^\circ$
rectangle	$2$	$2$	$180^\circ$
equilateral triangle	$3$	$3$	$120^\circ$
rhombus	$2$	$2$	$180^\circ$
parallelogram	$0$	$2$	$180^\circ$
kite	$1$	$1$
regular hexagon	$6$	$6$	$60^\circ$

📖 Worked example

The diagram shows a propeller shape. Write down its order of rotational symmetry.

Step 1 of 1

Turn the shape about its centre: in one full turn, how many times does it look exactly the same?

It looks the same every third of a turn.

\text{Order} = 3

📖 Worked example

The diagram shows an equilateral triangle. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

Step 1 of 2

Turn the shape about its centre: in one full turn, how many times does it look exactly the same?

It looks the same every third of a turn.

\text{Order} = 3

Practise this →

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