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

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  

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

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

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

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

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
  • 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

What terms related to circles do I need to know?

• Circles have several specific terms that you need to be familiar with:
  • 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 diameter is equal to 2 × the radius
  • A portion of the circumference is called an arc
  • A portion of the area, contained between two radii and an arc, is called a sector
  • A line between two points on the circumference is called a chord
  • The area formed between a chord and an arc is called a segment
  • A line which intersects the circumference at one point only, is called a tangent

• The ratio  is equal to π (3.14159...)
• Circles have many angle properties and you will need to learn some of them
  
  • These can be found in the revision note named Circle Theorems