Properties of Polygons (Cambridge (CIE) IGCSE International Maths) : Revision Note

Properties of Polygons

What are the names of common 2D shapes?

  • You should know the general names of all the 2D polygons

    • A triangle has 3 sides

    • A quadrilateral has 4 sides

    • A pentagon has 5 sides

    • A hexagon has 6 sides

    • A heptagon has 7 sides

    • An octagon has 8 sides

    • A nonagon has 9 sides

    • A decagon has 10 sides

    • A polygon is a flat (plane) shape with n straight sides

      • regular polygon has all sides the same length and all angles the same size  

Names of shapes with 3 to 10 sides

What are the names of the different types of triangles?

  • You should know the names and properties of the different types of triangles

    • An equilateral triangle has 3 equal sides and 3 equal angles

    • An isosceles triangle has 2 equal sides and 2 equal angles

    • A right-angled triangle has one 90° angle

    • A scalene triangle has 3 sides all of different lengths

MPfz1HV0_cie-igcse-core-rn-angles-in-triangles-diagram-2---types-of-triangles

What are the names of the different types of quadrilaterals?

  • You should know the names and properties of the different types of quadrilaterals

    • These are squares, rectangles, parallelograms, rhombuses, trapeziums and kites

types of quadrilaterals

What are the properties of rectangles and squares?

  • Rectangles and squares have four equal right angles (90°)

  • Rectangles have two pairs of equal length, parallel sides

    • Squares are just regular rectangles; all four of their sides are equal

  • The diagonals of a rectangle bisect each other at the centre of the rectangle

    • This means that they cut each other in half

    • The intersecting diagonals form two pairs of angles at the centre

      • In a square, all four of these angles will be equal to 90°

  • Pythagoras’ theorem can be used to find the length of the diagonal of a square or rectangle

    • The diagonal forms the hypotenuse of a right-angled triangle

Properties of a rectangle

What are the properties of parallelograms and rhombuses?

  • Parallelograms and rhombuses (rhombi) have two pairs of equal, opposite, angles

  • Parallelograms and rhombuses have two pairs of opposite, parallel sides

  • Rhombuses have four sides of the same length

    • This means a rhombus is a regular parallelogram

      • A square is also a regular rhombus

  • The diagonals of a parallelogram bisect each other, forming two pairs of opposite angles

  • The diagonals of a rhombus bisect each other at right angles (90°)

    • This means that they cut each other in half

    • The diagonals will not be of equal length

      • On the diagram below, the diagonal AC is shorter than the diagonal DB

Properties of parallelograms

What are the properties of trapeziums?

  • Trapeziums have one pair of opposite, parallel sides

    • These are not of equal length

  • Trapeziums may not have any equal angles

    • As with all quadrilaterals, the angles add up to 360°

  • If a trapezium has a line of symmetry, it is classed as isosceles

    • Isosceles trapeziums have two pairs of equal angles

    • The non-parallel sides in an isosceles trapezium will be equal length

    • An isosceles trapezium has two diagonals of equal length

Properties of trapeziums

What are the properties of kites?

  • Kites have one line of symmetry, known as their main diagonal

  • The angles opposite the main diagonal are equal

    • These are angles ABC and ADC on the diagram below

  • The diagonals of a kite bisect each other at right angles (90°)

    • This means that they cut each other in half

    • The diagonals will not be of equal length

  • Kites have no parallel sides

  • Kites have two pairs of equal length, adjacent sides

Properties of kites

Examiner Tips and Tricks

  • Remember the key facts about each type of shape

    • You may need to use these facts to help work out more tricky geometry problems

Worked Example

Complete each statement.

(i) A quadrilateral with only one pair of parallel sides is called a ................

A quadrilateral with only one pair of parallel sides is called a trapezium.

(ii) A quadrilateral with two pairs of parallel sides is called a ................ 

A quadrilateral with two pairs of parallel sides is called a parallelogram

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Jamie Wood

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