Pythagoras theorem
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
In one line: Right angle first, hypotenuse last.
Practice This ConceptUnderstand it
This theorem works only in a right triangle. The longest side, called the hypotenuse, is opposite the right angle, and that side must be used as c in the formula.
Formula and rule
c2 = a2 + b2, where c is the hypotenuse in a right triangle.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
In a right triangle with legs 9 cm and 12 cm, c² = 9² + 12² = 81 + 144 = 225, so c = 15 cm.
Method you can reuse
- 1Find the right angle.
- 2Mark the hypotenuse.
- 3Substitute the two known sides.
- 4Solve the square root carefully.
Sketch it in your answer
Draw the right angle mark first; the side opposite it is the hypotenuse.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
When can Pythagoras theorem be used in a triangle?
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Common wrong answer
Adding the three side lengths or using a non-hypotenuse side as c. That gives the wrong value.
Don't mix this up
Exam tip
Pythagoras theorem diagram
Open full screen to read every label clearly.
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
- 2
Add for 2 marks
Example: For a right triangle with legs 6 cm and 8 cm, the hypotenuse is 10 cm because 6² + 8² = 10².
- 3
Add for 3 marks
This theorem works only in a right triangle.
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