# Pythagoras Worksheet • Section 1 of the Pythagoras Theorem worksheet contains 36 skills-based Pythagoras Theorem questions, in 3 groups to support differentiation
• Section 2 contains 4 applied Pythagoras Theorem questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 3 foundation and higher level GCSE exam questions on Pythagoras Theorem
• Answers and a mark scheme for all Pythagoras Theorem questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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### Pythagoras Theorem at a glance

Pythagoras Theorem states that, in a right angled triangle abc, the square of the length of the hypotenuse (or longest side) c is equal to the sum of the squares of the lengths of the two shorter sides of the triangle, a and b. Its algebraic formula is a2+b2=c2. It is sometimes called the Pythagorean Theorem.

This result can be used to find the length of a missing side of a right angle triangle when the other two are known.

To find the length of the hypotenuse, square the lengths of the sides a and b, and add them. Finally, square root to find the length of the unknown side. To find the length of a missing shorter side (say a), square b and c. We then proceed by subtracting the square of b from the square of c, and taking the square root as before.

Square rooting will often result in non-terminating decimals so students should give their final answers to an appropriate number of decimal places or significant figures.

A Pythagorean triple is a set of three integers that satisfies Pythagoras theorem – for example, 3, 4, 5 or 6, 8, 10. It is useful for students to be able to spot these.

There are some common real life applications of Pythagoras that come up in exam questions, such as finding how far up a wall a ladder reaches.

Looking forward, students can then progress to additional geometry worksheets, for example a or an For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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