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.

Markus Hohenwarter, created with GeoGebra