Properties of Polygons (Edexcel IGCSE Maths)
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4.2C
Properties of polygons
What are the names of common 2D shapes?
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You should know the general names of all the 2D polygons
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A triangle has 3 sides
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A quadrilateral has 4 sides
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A pentagon has 5 sides
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A hexagon has 6 sides
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A heptagon has 7 sides
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An octagon has 8 sides
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A nonagon has 9 sides
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A decagon has 10 sides
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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
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Polygons
What are the names of the different types of triangles?
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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?
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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?
- A square is a rectangle where all the sides have the same length
- The table below shows the properties of a rectangle and square
Rectangle
| Rectangle | Square | |
|---|---|---|
| Sides | - Two pairs of equal, opposite sides - Two pairs of parallel sides | - All sides have the same length - Two pairs of parallel sides |
| Angles | - All angles are 90° | - All angles are 90° |
| Diagonals | - Both diagonals bisect each other - Diagonals have the same length | - Both diagonals bisect each other - Diagonals have the same length - Diagonals are perpendicular |
| Symmetries | - Two lines of symmetry - Order of rotational symmetry is two | - Four lines of symmetry - Order of rotational symmetry is four |
What are the properties of parallelograms and rhombuses?
- A rhombus is a parallelogram where all the sides have the same length
- The table below shows the properties of a parallelogram and rhombus
Parallelogram
| Parallelogram | Rhombus | |
|---|---|---|
| Sides | - Two pairs of equal, opposite sides - Two pairs of parallel sides | - All sides have the same length - Two pairs of parallel sides |
| Angles | - Two pairs of equal, opposite angles - Each pair of adjacent angles add up 180° | - Two pairs of equal, opposite angles - Each pair of adjacent angles add up 180° |
| Diagonals | - Both diagonals bisect each other | - Both diagonals bisect each other - Diagonals are perpendicular |
| Symmetries | - No lines of symmetry - Order of rotational symmetry is two | - Two lines of symmetry - Order of rotational symmetry is two |
What are the properties of trapeziums?
- The table below shows the properties of a trapezium and an isosceles trapezium
| Trapezium | Isosceles trapezium | |
|---|---|---|
| Sides | - One pair of parallel sides - The parallel sides have different lengths | - One pair of parallel sides - The parallel sides have different lengths - The non-parallel sides have the same length |
| Angles | - Two pairs of adjacent angles that add up to 180° | - Two pairs of adjacent angles that add up to 180° - Two pairs of adjacent angles that are equal |
| Diagonals | - Do not bisect each other | - Do not bisect each other - Diagonals have the same length |
| Symmetries | - No lines of symmetry - Order of rotational symmetry is one | - One line of symmetry - Order of rotational symmetry is one |
What are the properties of kites?
- The table below shows the properties of a kite
Kite
| Kite | |
|---|---|
| Sides | - Two pairs of equal, adjacent sides - No parallel sides |
| Angles | - One pair of equal, opposite angles |
| Diagonals | - One diagonal bisects the other - Diagonals are perpendicular |
| Symmetries | - One line of symmetry - Order of rotational symmetry is one |
Worked Example Complete each statement.
(i) A quadrilateral with only one pair of parallel sides is called a ................
Answer:
Final answer: 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 ................
Answer:
Final answer: A quadrilateral with two pairs of parallel sides is called a parallelogram.
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