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 circleparts
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
Exam Tip
Commit the facts and vocabulary in this revision note to memory
You will most likely need to use some of them to work out higher level geometry problems
Properties of 3D Shapes
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
Exam Tip
Remembering the properties of 3D shapes will help particularly with questions involving surface area