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The Pythagorean Theorem
For a right triangle with legs a and b and hypotenuse c, a²+b²=c².
How it works
For a right triangle with legs a and b and hypotenuse c, a²+b²=c². Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
Find the hypotenuse when the legs are 5 and 12.
- Square the legs: 25 and 144.
- Add: 25+144=169.
- Take the positive square root: √169=13.
The hypotenuse is 13.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Determine whether side lengths 8, 15 and 17 form a right triangle.
Questions learners ask
What is the key idea in the pythagorean theorem?
For a right triangle with legs a and b and hypotenuse c, a²+b²=c².
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.