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GCSE Pythagoras Theorem Questions and Answers

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Question 29 - AQA GCSE Foundation Maths Past Paper 2 November 2021

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Question 23 - AQA GCSE Higher 2020 Past Paper 2 - Geometry and Measures, Prisms, Volume & Surface Area, Pythagoras Theorem, Angles, Triangles, 3D Shapes Question By Topic

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Question 31 - OCR GCSE Higher 2020 Past Paper 5 - Ratio, Proportion and Rates of Change,Ratio & Proportion, Geometry and Measures,Trapeziums,Triangles,Area and Permieter,Pythagoras Theorem Question By Topic

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Question 18 - OCR GCSE Foundation 2020 Past Paper 1 - Geometry and Measures,Triangles,Pythagoras Theorem Question By Topic

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Question 29 - Edexcel GCSE Foundation 2020 Past Paper 3 - Geometry and Measures, Triangles, Circles, Sectors and Arcs, Area and Perimeter, Pythagoras Theorem Question By Topic

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Question 16 - OCR GCSE Foundation 2018 Past Paper 3 - Geometry and Measures, Pythagoras Theorem, Triangles Questions By Topic

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Question 26 - AQA GCSE Foundation Specimen Paper 2 - Geometry and Measures, Pythagoras Theorem, Questions By Topic

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Question 22 - AQA GCSE Foundation 2017 Past Paper 2 - Geometry and Measures, Pythagoras Theorem Questions By Topic

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Question 22 - Edexcel GCSE Foundation 2017 Past Paper 2 - Geometry and Measures, Pythagoras Theorem, Trigonometry Angles, Trigonometry Lengths, Trapeziums, Numbers, Rounding Numbers, Estimation, Significant Figures, Decimal Places Questions By Topic

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1 2 3
Everything about Pythagoras Theorem for the GCSE Exam!

1. What is Pythagoras Theorem

Pythagoras theorem states that the square of the Hypotenuse is equal to the sum of the squares of the other two sides. 

If the sides of the right-angled triangle are labelled a, b and c then Pythagoras' theorem states : a² + b² = c²

01. Pythagoras Theorem

In the above diagram, side c is known as the hypotenuse, the longest side of a right-angled triangle and is opposite the right angle. Side “a” and side “b” are known as the adjacent sides.

Note: The hypotenuse is always the longest side of the right angled triangle.

If any two sides of a right angled triangle are known, one can use Pythagoras theorem to work out the length of the third side.

1.1 How to use Pythagoras Theorem

In order to use Pythagoras theorem, first label the sides of the triangle. Next write down the formula and apply the numbers and finally work out the answer.

In order to use Pythagoras theorem to find hypotenuse for the given triangle:

02. Pythagoras Theorem

First label sides as a = 7 cm, b = 24 cm, c = c

It is very important to label the hypotenuse correctly with c. The adjacent sides, next to the right angle can be labelled a and b according to the size.

Next write down the formula a² + b² = c² 

Apply the numbers and finally work out the answer:

Pythagoras Theorem Image 01

Make sure you give your final answer in the correct form including units where appropriate.

1.2 Example Questions on Pythagoras theorem

Example 1: On finding the length of the hypotenuse 

Find x and give your answer to 4 significant figures:

03. Pythagoras Theorem

Solution: 

Pythagoras Theorem Image 02

Example 2: on finding an adjacent side.

Find x in the given triangle.

04. Pythagoras Theorem

Solution: 

Pythagoras Theorem Image 03

Example 3:

Find x in the given triangle.

05. Pythagoras Theorem

Solution: 

Pythagoras Theorem Image 04

Quiz Questions
GCSE Pythagoras Theorem

GCSE Topics

  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
  • Probability (258)
  • Statistical Measures (5)
  • Numbers (1,084)
    • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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