Maths dictionary
What is the Pythagorean theorem?
In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c².
Definition
In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c².
Example
A triangle with legs 3 and 4 has hypotenuse 5, because 9 + 16 = 25.
Tip
It only works for right-angled triangles.
Practise it
- Learn it visually: The Pythagorean Theorem (interactive lesson)
- Worksheets: Pythagorean theorem (Grade 8)
- Online maths practice
Quick check: try these
Work each one out on paper, then tap the question to see the answer.
A right triangle has legs of 10 and 24. The hypotenuse is
Answer: 26
A right triangle has legs of 9 and 40. The hypotenuse is
Answer: 41
A right triangle has legs of 40 and 42. The hypotenuse is
Answer: 58
A right triangle has legs of 6 and 8. The hypotenuse is
Answer: 10
Learn it in depth
Pythagorean theorem is part of Pythagoras Theorem for Class 7: notes, formulas, solved examples with every step, common mistakes and ten practice questions with answers. Want a teacher to go through it with you? See Class 7 maths tuition.
Related words
FAQ
Pythagorean theorem: questions
What is the Pythagorean theorem?
In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c². A triangle with legs 3 and 4 has hypotenuse 5, because 9 + 16 = 25.
What is a common mistake with pythagorean theorem?
It only works for right-angled triangles.
Where do students learn pythagorean theorem?
Pythagoras Theorem is usually taught in Class 7, and the ideas come back in later classes. Chapter names and order differ by board and textbook, so follow your own textbook. We have a full page with notes, solved examples and practice questions.
Play it, don't just read it
Try it now: Pythagorean theorem
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Pythagorean theorem (Grade 8): Finding a side of a right-angled triangle using a² + b² = c². Open the practice page or print a worksheet.
Or play a game
- Angle EstimatorGuess the size of an angle in degrees and see how close you were.Play
- Geometry ExplorerPractise area, volume, circles and right-triangle relationships with…Play
- The Pythagorean TheoremSee a² + b² = c² with squares on the sides of a right triangle.Play