Pythagoras

You see here four congruent right-angled triangles with sides a, b and hypotenuse c.

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1. What is the area of the square built by these four triangles (including the small square in the middle)? Make a sketch of the situation and write down your solution on paper.
2. Now drag the blue point counter-clockwise as far as possible. What is the area of the small red and the big blue square? Again, make a sketch of the situation and write down your solutions on paper.
3. Do you see any connection between the areas in task (1) and (2)? Write down your conjectures.