Pythagoras Area Lab

One square, four triangles, two arrangements — and the leftovers are equal

Free to use

91625

3² + 4² = 9 + 16 = 25 = 5²

Add your own title and footer on any paid plan.

What to show

The two legs

c = 5, a whole number — this is a Pythagorean triple.

Triples to try

Using it in class

  1. Start on “Squares on the sides” and drag a and b. Ask what the third number does before anyone says the formula.
  2. Switch to “Four pieces, one frame” and read the frame first: it is (a + b) by (a + b), and four triangles are about to come out of it.
  3. Flip between c² and a² + b². The frame does not move and the four triangles do not change — so the leftovers have to be equal. That is the proof, and it is the step the picture does rather than tells.
  4. The triple buttons give a whole-number c, which is worth reaching for the first time a class meets this. Dragging reaches everything else.