Pythagorean theorem — a² + b² = c²
"The most famous formula of school math: in a right triangle the two legs build squares whose areas together exactly fill the square on the hypotenuse. a² + b² = c² turns geometry into arithmetic."
What is this topic about?
The theorem only applies to RIGHT triangles: the square of the hypotenuse c equals the sum of the leg squares — a² + b² = c². It measures what a ruler cannot: the diagonal across a sports field (√(90² + 45²)), a ladder against a wall, distances on maps. Grade 8–9 trains both directions (hypotenuse from the legs, one leg from the other two) plus the converse test for right angles, and completing the squares makes the formula visible. Watch the classic traps: c is ALWAYS the side opposite the right angle, and triangles without a right angle need the law of cosines instead.
The best way to learn it
Find the right angle first — the side opposite it is c, everything else is a leg.
Estimate: c must be longer than each leg but shorter than their sum.
Keep the units squared inside the squares — only the final root returns to length units.
Frequently asked questions
Practise Pythagoras in a duel
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