One square, four triangles, two arrangements — and the leftovers are equal
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3² + 4² = 9 + 16 = 25 = 5²
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What to show
The two legs
c = 5, a whole number — this is a Pythagorean triple.
Triples to try
Using it in class
Start on “Squares on the sides” and drag a and b. Ask what the third number does before anyone says the formula.
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.
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.
The triple buttons give a whole-number c, which is worth reaching for the first time a class meets this. Dragging reaches everything else.