Prior Content: Angles (Including Parallel Lines) – in particular Angle Notation.
Possible Next Steps: Circle Theorems, 2D Area & Perimeter, Constructions, Similar Shapes, Transformations of Shapes, Basic Trigonometry
Contents
- 1.1 Names & Defining Polygons
- 2.1 Angles in a Triangle
- 2.2.1 Types of Triangles
- 2.2.2 Angles in Isosceles Triangles
- 3.1 Properties of Quadrilaterals
- 3.2 Angles in a Quadrilateral
- 4.1 Interior & Exterior Angles of a Polygon
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Names & Defining Polygons
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Names of 2D Shapes
Online Platforms (with Videos & Exercises)
- Khan Academy
- Properties of shapes & polygons: Videos & practice
Activities & Resources
- Pixi Maths
- Transum
- Go Teach Maths
- Standards Unit (DfES)
- Standards Unit SS1: Classifying Shapes (Standards Unit, DfES; PDF
Worksheets
- Corbettmaths
- 2D Shapes Practice Questions & Solutions
- 2D Shapes Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- CIMT MEP (online self-checking)
- MathsPad
Dr Frost Resources
Dr Frost Videos
K93: Know the Names of Polygons.
Dr Frost Slides & Activities
- All in one summary sheet
Exam Practice
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 25b: Know the names of polygons.
- 78a: Distinguish between regular and irregular polygons.
- 25: Exam Practice: Introduction to 2D shapes
- 78: Exam Practice: Properties of polygons
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.1 Angles in a Triangle
Teaching Videos, Exercises & Activities
Dr Frost Resources
Extension Materials
2.2.1 Types of Triangles
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Types of Triangles
Rob Mitchell
Image Source: http://mrferrell.pbworks.com
Online Platforms (with Videos & Exercises)
- Khan Academy
- Section with Videos and Practice Questions
Worksheets
- Corbettmaths
- Types of Triangle Practice Questions & Solutions
- Types of Triangle Worksheet & Solutions
- mathworksheets4kids Worksheets
- Math-aids.com create your own worksheet
- Maths 4 Everyone
Dr Frost Resources
Dr Frost Video
K94: Know the Names of Different Types of Triangle.
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 77a: Know the names of different types of triangles.
- 78e: Understand the definition of different triangles and their properties.
- 148a: Use the triangle inequality to reason about the lengths of sides of a triangle. (not yet active)
- 148b: Use the angle-side relationship to order the side lengths or angles of a triangle. (not yet active)
- 77: Exam Practice: Types of quadrilaterals and triangles
- 78: Exam Practice: Properties of polygons
- 148: Exam Practice: Properties of triangle lengths
Extension Materials
Activities
- Math = Love (Sarah Carter)
- BossMaths
- Desmos
- Polygraph: Triangles (vocabulary game: scalene, isosceles, equilateral, acute, obtuse, right)
2.2.2 Angles in Isosceles Triangles
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbettmaths Angles in a Triangle (From 3:35)
Khan Academy Isosceles Examples
Khan Academy Isosceles with Algebra
Khan Academy Isosceles with Algebra (Requires Knowledge of Parallel Lines)
Online Platforms (with Videos & Exercises)
- Go Teach Maths treasure trove of activities & ppts
- Khan Academy
Activities
- Maths 4 Everything
- Pixi Maths
- Don Steward
- Goal Free Problems
Got kids really struggling with isosceles triangles. Getting lots of ‘the top angle is the one that’s different’. Hoping these will support our lower attaining pupils in being able to think flexibly about the way angles, dashes and orientation are linked. pic.twitter.com/0XZi23YUAZ
— Dan Draper (@MrDraperMaths) February 3, 2021
Worksheets
- Dr Austin Maths
- Transum Online Worksheet 2
- Ed Southall Triangle angles worksheet everything in section 1 (TES Account Required)
- Corbettmaths
- Maths 4 Everyone
- Self Marking Sheets by Phil Rhodes
- Angles in Special Triangles Excel File
- Khan Academy
Dr Frost resources
Dr Frost Videos
Whole Topic Video
K301: Angles in an Isosceles Triangle
K302: Find an Angle in an Isosceles Triangle Using Angles on Parallel Lines.
Dr Frost Slides & Activities
Extra Questions
Exam Practice
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 150a: Determine an angle in an isosceles triangle given one of the other angles.
- 150b: Determine an angle in a diagram involving an isosceles triangle with an extended side.
- 150c: Determine an angle using multiple angle laws in a diagram that involves an isosceles triangle.
- 262i: Determine an angle in a triangle using angles on parallel lines.
- 150: Exam Practice: Base angles of an isosceles triangle
- 262: Exam Practice: Alternate, corresponding and co-interior angles
Further Practice
EXTENSION MATERIALS
Activities & Resources
- Mrdrapermaths presentation and exercises
- Mr Draper Maths Building Up Angle Reasoning
3.1 Properties of Quadrilaterals
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Names of Quadrilaterals
Online Platforms (with Videos & Exercises)
- cimt.org self contained notes and self checking questions
- Khan Academy
- Properties of quadrilaterals: Videos & practice
- Intro to quadrilaterals: Videos & practice
Activities & Resources
- Go Teach Maths treasure trove of activities & ppts
- Pixi Maths
- Andy Lutwyche
- Don Steward
- Quadrilaterals on a 6×6 Dotty Grid
- Quadrilaterals on a 3×3 Dotty Grid
- Quadrilaterals on a 5×5 Dotty Grid
- Grid Kites and Rhombuses
- Given the Sides, Make a Polygon
- Quadrilaterals on a Grid
- Complete the Quadrilateral
- Coordinates of Quadrilaterals
- Draw the Shape✦
- Creating Quadrilaterals
- 9 Isosceles Trapeziums
- Mid-points of Quadrilaterals
- Names of Quadrilaterals
- Named Quadrilaterals
- 8 Special Quadrilaterals
- The Chalkface
- Guess The Quadrilateral: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- Quadrilaterals Interactive: Interactive page
- PhET Interactive Simulations
- PhET Quadrilateral Interactive Simulation (embedded below)
- Transum
- Interactive Maths
- Squares: Is it a Square?
- Goal Free Problems
- Go Teach Maths
- thewessens.net Classroom Apps
- Quadrilateral Explorer (fold and rotate each quadrilateral to see its sides, angles, diagonals and symmetry)
- Desmos
- Polygraph: Basic Quadrilaterals (vocabulary game for quadrilateral properties)
- Polygraph: Advanced Quadrilaterals (harder version: kites, trapezia, parallelograms)
- Mathematics Assessment Project
- Lisa Bejarano
- emaths
- Shahira Ibrahim
- Jo Morgan
- Quadrilateral family tree✦ (by Jo Morgan)
- Ticktock Maths
- Recognising Quadrilaterals lesson (slides)
- Durham Maths Mysteries (Shirley Fall, Durham County Council)
- Properties of Shape Mystery · support cards · blank grid (card-sort mystery;
Worksheets
- Corbettmaths
- Quadrilaterals Practice Questions & Solutions
- Quadrilaterals Worksheet & Solutions
- Kuta Software Worksheet
- mh591 Properties of Quadrilaterals Matching Card Activity (TES Account Required)
- Unknown Author Quadrilaterals Research Sheet
- CIMT MEP (online self-checking)
- Miss Konstantine (MathsHKO)
- Kuta Software
- Access Maths
- MME
- Pret Homework (Tom Kendall)
- Quadrilateral Properties (Tom Kendall, pptx)
- Pret Homework (@Missgourlay)
- Quadrilaterals (@Missgourlay, pptx)
Dr Frost resources
Dr Frost Video
K96: Understand the Definition of Different 2D Shapes and Their Properties.
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
EXTENSION MATERIALS
Worksheets
- Kutasoftware Worksheet 1, Worksheet 2– use properties to find angles
- MissBrookesMaths Angles in quadrilaterals – equations
- Place all Quadrilateral types in a Venn Diagram, but use their shape to represent them. Solution below
3.2 Angles in a Quadrilateral
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Angles in a Quadrilateral
Online Platforms (with Videos & Exercises)
- Go Teach Maths treasure trove of activities & ppts
Activities
- Maths 4 Everyone
- interactive-maths.com random example (1 missing angle)
- Andy Lutwyche
- Don Steward
- The Chalkface
- Tessellation of quadrilaterals: Interactive page
- Goal Free Problems
- Ticktock Maths
- Angles in Quadrilaterals lesson (slides)
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
- Kuta Software
- Corbettmaths
- Missing Angles (Big) Practice Questions & Solutions
- Angles: Quadrilaterals Worksheet & Solutions
- Self Marking Sheets by Phil Rhodes
- Angles in Quadrilaterals Excel File
Dr Frost resources
Dr Frost Videos
Whole Topic Video
K309: Angles in a Quadrilateral
Exam Practice
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 151a: Determine an angle in a quadrilateral given its other angles.
- 151b: Determine an angle involving a quadrilateral with an extended side.
- 151c: Determine an angle in a kite.
- 151d: Determine an angle using multiple angle laws in a diagram that involves a quadrilateral.
- 262f: Determine angles in a parallelogram or rhombus.
- 262g: Determine angles in a trapezium.
- 262k: Determine an angle in a complex diagram involving a parallelogram or rhombus.
- 263g: Form and solve an equation using algebraic angles to determine an unknown angle in a parallelogram, rhombus or trapezium.
- 151: Exam Practice: Sum of angles in a quadrilateral
- 262: Exam Practice: Alternate, corresponding and co-interior angles
- 263: Exam Practice: Algebraic expressions and equations using angle facts
Further Practice
EXTENSION MATERIALS
4.1 Interior & Exterior Angles of a Polygon
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Angles in Polygons
Courtesy of Maths Genie
Corbett Maths Tessellations
Online Platforms (with Videos & Exercises)
- cimt.org self contained notes and self checking questions
- Khan Academy
Activities & Resources
- Go Teach Maths treasure trove of activities & ppts
- Mathspad Exterior Angle tool✦
- Pixi Maths
- Unknown Author Ppt going through basic principles & examples
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- Dissecting Regular Polygons into Rhombuses
- Regular Polygons with Algebra
- Regular Dodecagons
- Polygons and Isosceles Triangles
- Barn Roof Angles
- Regular Polygon Nesting
- Exterior Angles and Star Polygons
- Angles in Tessellations
- Ratio and Polygon Angles
- Polygon Angle Sum
- Constant Difference Angles
- Angles in Polygons by Chopping
- Inscribed Rhombus
- Surrounding a Point✦
- Fractions of Half Turns
- Regular Polygon Angles
- Isosceles Trapezia and Regular Polygons✦
- Pentagons and Angles✦
- Which Fit Better?
- Kites and Polygon Angles
- Star Polygons
- Flowers✦
- Nonagon Appreciation
- Ring Alignments
- Pentagon Angles
- Polygon Angles
- Transum
- Interactive Maths
- Angles in a Regular Polygon: GeoGebra
- Goal Free Problems
- Mr Draper Maths Exterior Angles of Convex Polygons✦
- Mr Draper Maths Concave Polygons
- Mr Draper Maths Interior Angle Sum Derivations
- Mr Draper Maths Reasoning With Interior Angles
- MathsPad
- The Chalkface
- Mathematics Assessment Project
- Interwoven Maths
- Using ratio to find angles in polygons✦ (by Stephen Gregory)
- GeoGebra
- Mathigon
- jamesgreenland
- Cazoom Maths
- Ticktock Maths
- Interior Angles of Polygons lesson (slides)
- Exterior Angles of Polygons lesson (slides)
- Pondering Planning in Mathematics (Paul Rowlandson)
Worksheets
- Dr Austin Maths
- Finding Regular Activity (Word | PDF | Answers)
- Regular Fill in the Blanks (Word | PDF | Answers)
- Regular Practice Strips (Word | PDF | Answers)
- Crack the Code (Word | PDF | Answers)
- Regular Practice Grid (Word | PDF✦ | Answers✦)
- Irregular Practice Strips (Word | PDF | Answers)
- Irregular Practice Grid (Word | PDF✦ | Answers✦)
- Regular Practice Strips (Word | PDF | Answers)
- Regular Practice Strips (Word | PDF | Answers)
- Revision Practice Grid (Word | PDF | Answers)
- Corbettmaths
- Angles in Polygons Practice Questions & Solutions
- Angles in Polygons Worksheet & Solutions
- Tessellations Practice Questions & Solutions
- Tessellations Worksheet & Solutions
- Kuta Software Worksheets 1 (Intro), 2 (Regular)
- Maths 4 Everyone
- Review Sheet
- Angles in Polygons: Challenges Sheet 1 · Challenges Sheet 2 · Challenges Sheet 3 · Challenges Sheet 4
- Angles in Polygons GCSE Questions and Solutions
- Pixi Maths
- Transum Online Worksheets
- Maths Genie
- Angles in Polygons: Booklet · Worksheet · Solutions · Lesson · Topic page
- Mathsaurus (Kevin Olding)
- Naiker Maths
- Angles in Polygons: Worksheet
- Access Maths
- MME
- 1st Class Maths
- Mr Morley Maths
- Interior and Exterior Angles of Polygons: Notes jotter/worksheet · How-to sheet
- Pret Homework (@MissBsResources)
- Angles in Polygons (@MissBsResources, pdf)
- Pret Homework (Jo Morgan)
- Angles in Polygons✦ (Jo Morgan, docx)
Dr Frost resources
Dr Frost Videos
Whole Topic Video
K479: Find Missing Angles in a Non-Regular Polygon.
K477: Find the Size of the Exterior Angles of a Regular Polygon.
K480: Find the Size of the Interior Angles of a Regular Polygon.
K478: Find the Number of Sides of a Regular Polygon Given the Size of its Exterior Angles.
K481: Find the Number of Sides of a Regular Polygon Given the Size of its Interior Angles.
Dr Frost Slides & Activities
Exam Practice
Extra Questions
- Dr Frost Questions (Big)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 261a: Calculate the interior angle sum of a polygon given its number of sides.
- 261b: Determine missing angles in a non-regular polygon.
- 261c: Determine interior angles of a polygon where there is a relationship given between some angles.
- 261d: Calculate the size of the exterior angles of a regular polygon.
- 261e: Calculate the size of the interior angles of a regular polygon.
- 261f: Determine the remaining angle around a point where two or more polygons meet.
- 261g: Determine an angle formed in a shape using sides or extended sides of polygons.
- 261h: Determine the number of sides of a regular polygon given the size of its exterior angles.
- 261i: Determine the number of sides of a regular polygon given the size of its interior angles.
- 261j: Determine the number of sides of a polygon given a ratio between its interior and exterior angles.
- 261k: Determine angles in polygons within regular polygons.
- 261l: Determine if a regular polygon will tessellate.
- 261m: Determine the number of sides of an unknown regular polygon required to complete a tessellation.
- 261n: Write a geometric proof using angle facts, including those for polygons.
- 263i: Form and solve an equation using algebraic angles to determine an unknown angle in a polygon.
- 261: Exam Practice: Interior and exterior angles of regular and irregular polygons
- 263: Exam Practice: Algebraic expressions and equations using angle facts
Further Practice
EXTENSION MATERIALS
Worksheets
- ItsMattKennedy Angle Chasing II – Polygons and Parallel Lines✦ (TES Account Required)
- mrorr-isageek.com Polygon Pile Up✦
Whole Topic Summary Resources (Including Past Paper Questions)
Download Angles in Polygons PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Angles in polygons as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
- Andy Lutwyche
- MathedUp
- Properties & Naming of 2D Shapes: Worksheet · Practice · Quiz · Question Gallery
- Physics & Maths Tutor
Activities
- NRICH (student problems)
- Don Steward
- Go Teach Maths
External
- NCETM
- NCETM Checkpoints: Geometrical properties: polygons (diagnostic tasks)
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.