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Discovering Pythagoras' Theorem

Experiment with the sliders to change the width and height of this right-angled triangle. Watch what happens to the areas of the squares. What do you notice? How might that let you predict the length of the longest side c (the hypotenuse) from the width a and height b ?
If you set the width to 8 and height to 6, what will the three square areas be? So what length will the hypotenuse c be in this triangle? The sliders won't allow it, but suppose I could set a width a = 12 and height b = 5. What would the hypotenuse c be now? Why? What if I set a = 7 and b = 24? Can you write a general rule about how c is connected to a and b? Can you write that rule in algebra?