An interactive lesson in three parts
Over 2,500 years ago, the Greek mathematician Pythagoras noticed something remarkable about every right triangle — a triangle with one perfect 90° corner.
No matter how big or small, those three sides always obey one rule:
Think of it this way: if you draw a square on each side of the triangle, the two smaller squares together have exactly the same area as the big square. Use the sliders below to watch that happen live!
Drag the sliders to change the legs. Notice how the three coloured squares always balance — the blue + green always equals the orange.
🔑 Unlock Part 2
Try setting the sliders! Or: 6² + 8² = 36 + 64 = 100. What number squared equals 100?
Grab the orange dot and drag it anywhere. The right-angle corner stays locked — and no matter the shape, a² + b² = c² never breaks.
☝ Drag the orange dotWe know a = 5 and b = 12. So:
Fill in any two of the three sides and leave one blank. Hit Calculate to find the missing value.
🔑 Unlock Part 3
The diagonal cuts the square into two right triangles. Both legs = 90 ft.
A Pythagorean Triple is a set of three whole numbers that perfectly satisfy a² + b² = c². Ancient builders used the 3–4–5 triple to construct perfect right angles without any measuring tools. Click any card to see the verification and load it into the checker below!
Enter any three positive numbers. The largest will be treated as the hypotenuse. Is it a triple?
🏆 Final Challenge
The diagonal is the hypotenuse. Both legs are given — and the answer is a whole number!