2D & 3D Shapes (CIE IGCSE Maths: Extended)

You will need to remember the names and properties of shapes 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 polygon is a flat (plane) shape with n straight sides
• 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

• 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 
• You should know the names and properties of circles and circle parts

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
• For example, a circle's perimeter is called a circumference and its line of symmetry is called a diameter
• The ratio  is equal to π
• Circles have many angle properties
• See section 3.4 Circle theorems!

You will need to remember the names and properties of many 3D shapes, the number of faces they have, the shapes of the faces and where they have planes of symmetry.

What 3D shapes should I know?

• You should know the general names of prisms
• A prism is a 3D shape with the same cross-section throughout
• The cross-section of a cube is a square
• The cross-section of a cuboid is a rectangle
• The cross-section of a cylinder is a circle
• You will also have to work with other prisms, such as triangular prisms
• In these cases the exam question will make sure the shape of the cross-section is clear
• You should know the names and properties of the different types of pyramids
• A pyramid has a flat base with sloping sides that meet at a point at the top
• The base will be a 2D shape
• Most pyramids are named after the shape of their base
• e.g. a square–based pyramid
• Some pyramids have special names you should know
• A cone has a circular base
• A tetrahedron’s base is an equilateral triangle
• You should know the name and properties of a sphere

What are the properties of 3D shapes?

• 3D shapes have a number of faces, vertices and edges
• A face is an individual surface of the 3D shape
• A vertex (plural, vertices) is a corner of the 3D shape
• An edge joins one vertex to another
• You should know the number and shape of the faces for the common 3D shapes
• A cube has 6 equal, square faces
• A cuboid has 3 pairs of equal, rectangular faces
• A cylinder has two equal circular faces and one rectangular face (its curved surface area)
• A triangular prism has two equal triangular faces and three rectangular faces
• If the triangular faces are equilateral then all of the rectangles will be equal
• If the triangular faces are isosceles then two of the rectangles will be equal
• A square-based pyramid has one square face and four equal triangular faces
• A tetrahedron has four triangular faces
• 3D shapes can be unfolded into a net to display their faces in 2D
• A net is just a pattern that could be folded to make the 3D shape