Pythagoras, trigonometry, similarity and congruency

Discover our collection of GCSE Pythagoras, trigonometry, similarity and congruency lessons, activities, powerpoints and notes. These resources are hand-picked by the Tes Maths Panel for their relevance to the 9-1 specifications - use them for planning, homework and revision.

This page contains the very best resources for teaching sections G5, G6 and G19 to G23 from the GCSE maths specification (first examined in 2017), combining structured lessons and engaging activities. With right-angled trigonometry now a key component of the foundation specification, it is more important than ever that all students develop competency in this area. This collection of resources and activities should help.

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Maths Pythagoras - Hypotenuse game

A game I made as a revision tool for covering the topic of Pythagoras' Theorem with my year 9s and 10s. Pupils reveal squares with questions hidden behind them which they must work out. Great for a starter/plenary activity.
By Daniel Burke

New GCSE Problem Solving: Problem 1 - Wooden Fence Post (Grade 7/8)

This is a problem aimed at higher attaining GCSE students. The premise of this resource is to revise multiple topics simultaneously through problem solving. This topic covers:
1. Basic Trigonometry
2. Surface Area
3. Circumference
4. Ratio
5. Pythagoras; Theorem

Solutions are also attached.

Any questions or ideas, feel free to get in contact!
By andy_gillen

3D Coordinates

3 worksheets on 3D coordinates where x and y axes remain in the same position as 2D. Variety of questions increasing in difficulty as they progress. Worksheets incorporate other topics such as area, volume, Pythagoras and trigonometry.

Answer sheets scanned in too.
By JamesCMartin

Pythagoras - Perigal's Disection

This is my favourite way to introduce Pythagoras to students. Included is a worksheet with the required pieces, the larger one for students to cut up and rearrange, the smaller one to stick in whole to write notes about what they have discovered. The PowerPoints give the instructions for how to cut up the larger shape and what to do and then the answer and the explanatory notes that lead to Pythagoras' Theorem
By MathSparks


Identifying Trigonometry ratio bingo

A bingo style activity to reflect on which trigonometric ratio to use given certain sides/angles within right-angles triangles.

To be used as a plenary to a start lesson or as a main reflection activity when putting trig ratios into practice.

N.b. I am an NQT so all feedback is welcomed for my shared resources.
By rpwelch32

3D Trigonometry

Powerpoint to be used to explain how to use Trigonometry in 3D shapes. Includes a starter, main explanation and a plenary. If you like this resource then please check out my other stuff on here! :)
By Owen134866

Trigonometry Speed Dating Task

Pupils work in groups to devise a good, clear explanation of how to use different trigonometric skills . Pupils then are put into different groups, where each person has 2 minutes to deliver their explanation and examples and answer any questions which arise. The PowerPoint was used to make them think about when, why and how it is used. The worksheet was used for pupils to collect together the information at the end.
By EmMakysm

Exact value of trigonometric ratios

Special triangles

PowerPoint and worksheet explaining where special trig ratios come from. I created these for use with my Y11 class who are taking Level 2 Certificate in Further Maths. To print of worksheet, must click 'print to scale'.
By danbar1000

Finding and applying the 3 trigonometric ratios - GCSE Mathematics 1 - 9 (NEW CONTENT)

Full lesson on finding and using the 3 trigonometric ratios that has been added to the new GCSE Maths specification.

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Visit for

- Lessons and worksheets suitable for the 9 - 1 GCSE Specification
- A-Level teaching resources for Core 1, Core 2, Core 3, Core 4, Decision 1 and Statistics 1
- Teaching resources for Level 3 Core Mathematics
- Schemes of work for Higher and Foundation GCSE Maths (adapted for the 9 - 1 specification)
- Topic tests for GCSE Maths and A-Level Maths
- Support for the teaching and coursework in GCSE Statistics
By We Teach - FREE Trial

Finding Exact Trig Values - Discovery Learning

This worksheet encourages students to become familiar with 'special triangles' to calculate exact trig values without a calculator. By focusing on multiples of 30, 45 and 60, it also helps students spot symmetry in graphs. I created this resources to introduce double angle formula/additonal formula. Answers attached :)
By emcnicholl

Exact Trigonometric Results - Codebreaker

Just a quick starter/plenary on exact results from trigonometry. The usual lame joke is the answer.
By alutwyche

Sine and cosine rule and area of triangles

Powerpoint Notes-Trigonometry-Sine & Cosine Rules

A few years ago I wrote a set of notes for pupils and put them on my website. The notes were supposed to be written in a pupil-friendly way, and different to notes students might find in textbooks or elsewhere on the internet. I have converted the notes to PowerPoint slides so you can download them, adapt them if needed, use them in revision lessons or perhaps give your students a set to take home with them to help them prepare for exams. The chances are there will be a few mistakes here and there, so if you spot any please email me & I will correct them. Hope they are of use!
By MrBartonMaths

Multistep non right angled triangles sine cosine

Multistep exam questions for non-right-angled triangles. Students need to select Sine Rule, Cosine Rule, 0.5ab sinC, Bearings on questions. Answers follow questions.
By mhorrocks87

Game of Thrones Cosine Rule

This is a (slightly) modified version of the excellent resource here by Cameron Wilford ( I changed the places, added a couple more questions and added a code for the students to find. Designed to test students using the cosine rule (both angle and side). It was surprisingly popular - and enlivened an otherwise slightly dry topic.
If you like my resources then please check out the The British International School Phuket website: for maths articles, ideas for gifted and talented students, maths videos and even a school code breaking challenge. All free!
By andrewchambers

2D similar shapes

Similar Triangles Challenge/Extension Q

An old chestnut. Good as an extension or a challenge. I use it at the end of a lesson to see which pairs of similar triangles they can see (there are many). I find that many pupils correctly guess the height (2/3) but are unable to prove it. The steps in this PowerPoint should help.
By mattfriend1

Similar Triangles

Differentiated task with answers.
By blod19

Congruent and Similar Shapes

Congruent and Similar Shapes
By ygbjammy

Trigonometry Intro Investigation

These two worksheets should be printed out. It has been scaled so that when pupils measure with a ruler each 'box' is 1cm x 1cm. Pupils take the required measurements and are asked if they have observed any similarities between O/A. The tan ratio is then introduced! Lots of calculator use is encouraged. Find out the tan of 30º, what about 45º? 1? What does that mean? Feedback would be appreciated as I am a student teacher.
By mallan824

Area and volume scale factor

Area and Volume Scale Factor

These are two PPTs I made to teach area and volume scale factors, including going from a VSF to an area or an ASF to a volume.
By Daniel Burke

Area and volume scale factors structured sheet

Write on sheet designed to make links between length, area and volume scale factors more obvious. I used it successfully with a middle set Year 9.
By nottcl

Ratio of Length, Area and Volume of similar shapes

GCSE Grade A topic / Functional Skills Introducing the concepts of Length Scale Factor, Area Scale Factor and Volume Scale Factor.
By nnyang

General Higher Tier GCSE Maths Revision - based around a box... Printable PowerPoint with answers

Students are presented with a diagram of a cuboid with unknown dimensions (feel free to provide an actual cuboid). They then solve 20 different Higher Tier revision questions based on: volume, unit conversions, similar shapes, enlargements, percentages, standard form, 3D Pythagoras, bounds, surface area, trial & improvement, solving quadratics by factorisation, solving quadratics using the formula, fractions & surds.

Printable Powerpoint with answers.
By philfallout


GCSE maths: Congruent trangles game cards.

These cards encourage students to explore which triangles they can copy to produce congruent triangles. If they cannot they are then asked what information they require. I use this after some work where I give students a triangle with no measurements written on it and challenge them to draw a congruent triangle. Discussion usually leads to talk of SSS, ASA and SAS.
By mrslack_maths

GCSE - Congruent Triangle Proofs

Comes with Powerpoint and worksheet. Includes harder follow up questions where you use a completed congruence proof to make subsequent justifications.
By DrFrostMaths

Congruence Snap

Use these snap cards to apply the definition of congruence. The cards also include a set of blank cards for students to create any missing cards or create their own. Open up the task by asking 'How many ways could I produce a congruent image of...'
By mrslack_maths