Properties of 2D Shapes (CIE IGCSE Maths: Core)

You will need to remember the names and properties of polygons in 2D, including where they have equal sides and angles, how their diagonals intersect, which angles are equal and where they have lines of symmetry.

What 2D shapes should I know?

• 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 equal size sides and angles  

• 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 triangle has one 90° angle
• You should know the names and properties of the different types of quadrilaterals
• These are squares, rectangles, parallelograms, rhombuses, trapeziums and kites

What are the properties of rectangles and squares?

• Rectangles and squares have four equal right angles (90°)
• Rectangles have two pairs of equal, 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
• There will be two pairs of angles at this point
• For a rectangle, one pair of obtuse angles and one pair of acute angles
• For a square, all four angles will be equal to 90°
• Pythagoras’ theorem can be used to find the length of the diagonal of a square or 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
• Rhombuses are also parallelograms, but they are not regular as they do not have four equal angles
• A square is 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

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

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
• 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, adjacent sides

What are the properties of circles?

• Circles are different to other 2D shapes and you must be familiar with their vocabulary
• A circle's perimeter is called a circumference
• Its line of symmetry is called a diameter
• The line from the centre of the circle to its circumference is called a radius

• The ratio  is equal to π
• Circles have many angle properties and you will need to learn some of them