Pythagoras

The most famous proof

An interactive lesson with 9 steps, about 8 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• In a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
• Rearranging four triangles inside a square proves it for every right triangle.
• The converse: if $a^2 + b^2 = c^2$, the angle opposite $c$ is a right angle.

Steps

1. The shortcut
2. Squares on the sides
3. A proof you can see
4. Shear, slide, shear
5. Find the hypotenuse
6. Find a leg
7. Is it right?
8. Distance between points
9. Ladder