GCSEMaths: FoundationEdexcelRevision NotesGeometry & Measures2D & 3D Shapes2D Shapes

2D Shapes (Edexcel GCSE Maths: Foundation)

Revision Note

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Jamie W

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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
      • A regular polygon has all sides the same length and all angles the same size  
    • A circle is not a polygon, as it has no straight edges
      • See Circles, Arcs & Sectors for more about circles

Names of shapes with 3 to 10 sides

Properties of Triangles

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

Worked example

In triangle ABC, one angle is 62° and another is 56°. Determine if ABC is equilateral, isosceles, or scalene.

Using the sum of angles in a triangle, which is 180°

180 - 56 - 62 = 62

This means two of the angles are the same

Angles are 56°, 62°, and 62°

Triangle ABC is isosceles

Properties of Quadrilaterals

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

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 W

    Author: Jamie W

    Expertise: Maths

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.