GCSEMathsOCRFoundationRevision Notes8. Basic Geometry2D & 3D ShapesProperties of Polygons

Properties of Polygons (OCR GCSE Maths): Revision Note

Exam code: J560

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on

OCR Maths: FoundationWJEC Eduqas Maths: FoundationAQA Maths: FoundationEdexcel Maths: FoundationWJEC Maths & Numeracy (Double Award): FoundationWJEC Maths & Numeracy (Double Award): HigherWJEC Eduqas Maths: HigherOCR Maths: HigherAQA Maths: HigherEdexcel Maths: Higher

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  

Names of shapes with 3 to 10 sides
Polygons

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

MPfz1HV0_cie-igcse-core-rn-angles-in-triangles-diagram-2---types-of-triangles

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

types of quadrilaterals

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

Properties of a rectangle
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

Properties of a parallelogram.
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

Properties of trapezia.

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

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:

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:

A quadrilateral with two pairs of parallel sides is called a parallelogram. 

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Author
Reviewer
Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.