Prior Content: Angles (Including Parallel Lines), Angles in Polygons, Constructions, 2D Area & Perimeter, Ratio & Basic Proportion (Including Conversions), Algebraic Proof
Possible Next Steps: Circle Theorems, Transformations of Shapes, Advanced Trigonometry
Contents
- 1.1 What Makes Shapes Similar?
- 1.2 Scale Factors
- 2.1 Congruence
- 2.2 Congruent Triangles
- 3.1 Area Scale Factors
- 3.2 Volume Scale Factors
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 What Makes Shapes Similar?
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – Similar Shapes by Cognito
DIFFERENCE BETWEEN SIMILAR & CONGRUENT FIGURES? by Mashup Math
l Videos
Corbett Maths Congruent & Similar Shapes
Online Platforms (with Videos & Exercises)
- Khan Academy
- Intro to similar triangles: Videos & practice
Activities & Resources
- Miss Konstantine (MathsHKO)
- The Chalkface
- The Silver Rectangle: PDF
- Ben Sparks (GeoGebra)
- Similar Triangles?: GeoGebra
- BossMaths
- NCETM
- NCETM Key Idea: Similar shapes (PowerPoint)
Worksheets
- CIMT MEP (online self-checking)
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 291a: Determine an angle in a shape similar to another.
- 291b: Determine an angle in a shape similar to another with unknown angles.
- 291d: Identify similar shapes.
- 291e: Determine if two shapes are similar given their lengths.
- 471g: Prove that two triangles are similar using AAA. (not yet active)
- 291: Exam Practice: Properties of similar shapes
- 471: Exam Practice: Proving triangle congruence using SSS, SAS, ASA and RHS
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.2 Scale Factors
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Similar Shapes – Missing Sides
Online Platforms (with Videos & Exercises)
- Khan Academy
- Solving similar triangles: Videos & practice
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- Ratio and Right Angled Triangles
- Similar Triangles (CBSE)
- Biggest Square Inside a Right Triangle
- Two Similar Shapes on a Grid
- Drawing Similar Triangles
- Perpendicular to the Hypotenuse
- Similar Pairs
- Two Similar Triangles
- Meeting Point?
- Similar Triangle Triples
- Geometric Mean in a Right Angled Triangle
- Giant Chairs
- Similar Triangles
- The Chalkface
- Sun, Moon and Coin: PowerPoint
- Mountain: PDF
- Transum
- Goal Free Problems
- Go Teach Maths
- Mathematics Assessment Project
- steele1989
Worksheets
- Dr Austin Maths
- Corbettmaths
- Similar Shapes: Sides Practice Questions & Solutions
- Similar Shapes: Sides Worksheet & Solutions
- Pixi Maths
- WW Similar Triangles Worksheet Word Doc or PDF
- Maths Genie
- Similar Shapes (Lengths): Booklet · Worksheet · Solutions · Lesson · Topic page
- Kuta Software
- Physics & Maths Tutor
- MME
- 1st Class Maths
- martahidegkuti
- @taylorda01
- Mr Morley Maths
- Similar Shapes (Lengths): Notes jotter/worksheet · Exam questions · Mark scheme
- Pret Homework (@AdamGoodridge18)
- Similar Triangles (@AdamGoodridge18, pptx)
Dr Frost Resources
Dr Frost Video
K520: Find Unknown Lengths Given Two Separate Similar Shapes.
K521: Find Unknown Lengths Given Two Similar Triangles With One Vertex in Common.
K522: Find Unknown Lengths Given Two Similar Shapes Where One is Inscribed the Other.
K523: Find Unknown Lengths Given Two Similar Shapes Where One is Inscribed the Other and Requires Subtraction.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 291c: Determine the scale factor between two similar shapes.
- 292a: Determine unknown lengths given two separate similar shapes.
- 292b: Determine unknown lengths given two similar triangles with one vertex in common.
- 292c: Determine unknown lengths given two similar shapes where one is inscribed inside the other.
- 292d: Determine unknown side lengths given two similar shapes and information about their perimeters.
- 292e: Calculate the amount of trimming required when enlarging an image from one size to another.
- 292f: Determine unknown lengths given two similar shapes where one is inscribed inside the other and requires subtraction.
- 292g: Determine an unknown shorter length on the coinciding side of one shape inscribed inside another.
- 292h: Determine a length using similar triangles combined with Pythagoras’ theorem.
- 292i: Use similar triangles to split a length in a ratio.
- 291: Exam Practice: Properties of similar shapes
- 292: Exam Practice: Determine unknown lengths in similar shapes
Further Practice
- Practise Questions
Extension Materials
Enrichment Video
Stand-up Maths: The A4 Paper Puzzle
Worksheet
2.1 Congruence
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – Congruent Shapes by Cognito
Congruent and Similar Triangles by Khan Academy
Corbett Maths Congruent & Similar Shapes
Online Platforms (with Videos & Exercises)
- Khan Academy
- Congruence & transformations: Videos & practice
Activities & Resources
- Don Steward
- Transum
- BossMaths
Worksheets
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 290a: Identify congruent shapes.
- 290b: Identify angles and lengths in congruent shapes.
- 290: Exam Practice: Properties of congruent shapes
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.2 Congruent Triangles
Teaching Videos, Exercises & Activities
Tutorial Videos
GCSE Maths – Congruent Triangle Rules by Cognito
Congruent Triangles by Maths Genie
Congruent Triangle Proof | Grade 5+ Crossover | GCSE Maths Tutor by The GCSE Maths Tutor
GCSE Tutorial Congruent Triangles Proof GCSE Maths Higher SSS, SAS, ASA, RHS by ukmathsteacher
Corbett Maths Congruent Triangles
Online Platforms (with Videos & Exercises)
- Khan Academy
- Congruent triangles: Videos & practice
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Don Steward
- Transum
- Go Teach Maths
- thewessens.net Classroom Apps
- Triangle Explorer (lock sides and angles to discover the congruence conditions)
- Mathematics Assessment Project
Worksheets
- Corbettmaths
- Congruent Triangles Practice Questions & Solutions
- Congruent Triangles Worksheet & Solutions
- Miss Konstantine Worksheet
- Pixi Maths
- Dr Austin Maths
- Maths Genie
- Congruent Triangles: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- Congruent Triangles: Worksheet
- Physics & Maths Tutor
- OCR
- Mr Morley Maths
- Congruent Triangles: Notes jotter/worksheet · Exam questions · Mark scheme
- WW Congruent Triangles Pairing PDF & ppt (with Solutions)
Dr Frost Resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 290c: Identify whether two triangles are congruent by SSS, SAS, ASA or RHS.
- 471a: Prove that two triangles are congruent using SSS.
- 471b: Prove that two triangles are congruent using ASA.
- 471c: Prove that two triangles are congruent using SAS.
- 471d: Prove that two triangles are congruent using RHS.
- 471e: Use circle theorems to prove that two triangles are congruent. (not yet active)
- 471f: Prove that side lengths/angles are equal by first proving congruence. (not yet active)
- 290: Exam Practice: Properties of congruent shapes
- 471: Exam Practice: Proving triangle congruence using SSS, SAS, ASA and RHS
Further Practice
- Practise Questions
Extension Materials
Worksheet
3.1 Area Scale Factors
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Similar Shapes: Area
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Similar Shapes ppt (Area SF Taught with Volume SF)
- Andy Lutwyche
- Don Steward
- The Chalkface
- Transum
- Go Teach Maths
- BossMaths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Maths 4 Everyone
- WW Similar Triangles Part 2 Worksheet Word Doc or PDF
- CIMT MEP (online self-checking)
- Maths Genie
- Similar Shapes (Area and Volume): Booklet · Worksheet · Solutions · Lesson · Topic page
- Physics & Maths Tutor
- MME
- Mr Morley Maths
- Similar Shapes (Area and Volume): Notes jotter/worksheet · Exam questions · Mark scheme
Dr Frost Resources
Dr Frost Video
K524: Relationship Between Scale Factors of Length and Area.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 324a: Determine the scale factor of area for two similar shapes given the scale factor of length.
- 324b: Determine the area of a shape, given the area of a similar shape and a length on each.
- 324c: Determine an unknown length of a shape, given the area of two similar shapes and one of their side lengths.
- 324m: Determine an actual area given an area on the map.
- 324n: Determine an area on a map given the actual area.
- 324o: Determine an area for inscribed triangles.
- 324p: Form an equation relating areas in inscribed triangles.
- 324q: Use the area of a shape to determine the increase in area to a similar shape that it is inscribed in.
- 324r: Use the area of a shape to determine the increase in area from a similar shape inscribed in it.
- 324s: Use the area of increase from an enlarged shape to determine the area of the original shape.
- 324: Exam Practice: Relationship between scale factors of length, area and volume
Further Practice
- Practise Questions
Extension Materials
Worksheet
3.2 Volume Scale Factors
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Similar Shapes: Volumes
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Similar Shapes ppt (Area SF Taught with Volume SF)
- Andy Lutwyche
- Miss Konstantine (MathsHKO)
- Don Steward
- Go Teach Maths
Worksheets
- Dr Austin Maths
- Areas and Volumes Fill In The Blanks (Word | PDF✦ | Answers✦)
- Areas and Volumes Practice Strips (Word | PDF✦ | Answers✦)
- Harder Areas and Volumes Fill In The Blanks (Word | PDF✦ | Answers✦)
- Harder Areas and Volumes Practice Strips (Word | PDF✦ | Answers✦)
- Revision Practice Grid (Word | PDF | Answers)
- Corbettmaths
- Similar Shapes: Area & Volume Practice Questions & Solutions
- Similar Shapes: Area & Volume Worksheet & Solutions
- Pixi Maths
- Mathshelper (Jon Stone)
- 1st Class Maths
Dr Frost Resources
Dr Frost Video
K525: Relationship Between Scale Factors of Length and Volume.
K526: Find the Surface Area of a Similar Solid When the Volumes are Given.
K527: Find the Volume of a Similar Solid When the Surface Areas are Given.
K528: Find the Surface Area/Volume of a Similar Solid When the Scale Factor of Surface Area/Volume is Given in Ratio Form.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- 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
- 324d: Determine the scale factor of volume for two similar solids given the scale factor of length.
- 324e: Determine the volume of a solid, given the volume of a similar solid and a length on each.
- 324f: Determine an unknown length of a solid, given the volume of two similar solids and one of their side lengths.
- 324g: Determine the surface area of a similar solid when the volumes are given.
- 324h: Determine the volume of a similar solid when the surface areas are given.
- 324i: Determine the length/surface area/volume for a similar solid when the scale factor is given in ratio form.
- 324j: Determine the ratio of the length/surface area/volume for two similar solids given a scale factor of another quantity.
- 324k: Solve problems involving two similar solids when the scale factor for length/surface area/volume is given in percentage difference form.
- 324l: Appreciate that scale factor of mass is the same as scale factor of volume where the material is the same.
- 324t: Solve problems involving similarity of a frustum and its original cone or pyramid.
- 324: Exam Practice: Relationship between scale factors of length, area and volume
Further Practice
- Practise Questions
Extension Materials
Worksheet
Whole Topic Summary Resources (Including Past Paper Questions)
Download Similar Shapes 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
- Similarity and congruence as PowerPoint or PDF
Worksheets
- Maths 4 Everyone
- MathedUp
- Similar Shapes: Area & Volume Scale Factors: Worksheet · Practice · Quiz · Question Gallery
- Congruent Triangles: Worksheet · Practice · Quiz · Question Gallery
- Similar Shapes (Area & Volume): Worksheet · Practice · Quiz · Question Gallery
- Congruence Proof: Worksheet · Practice · Question Gallery
- Mathsaurus (Kevin Olding)
- tumshy (David T)
- 1st Class Maths
- OCR
- Dr Frost
Activities
- Don Steward
- Intersections
- Similarity slides✦ (original by Don Steward; copy hosted on Jo Morgan’s Drive)
- The Chalkface
- Mr Thompson Maths
- MathsPad
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.