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
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
- This means a rhombus is a regular parallelogram
- 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
Examiner Tip
- Remember the key facts about each type of shape
- You may need to use these facts to help work out more tricky geometry problems
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.