For the proof outlined below, follow the directions at each step, and answer the questions as you work. When you are finished, you will have constructed a proof of the Pythagorean theorem. Note 2
Step 1: Construct an arbitrary right triangle that is not isosceles. Label the short leg a, the long leg b, and the hypotenuse c.
The proof still works if the triangle is isosceles -- that is if a = b -- but it is always better to work through a proof with an example that is not special in any way.
Step 2: Construct two squares whose sides have length a + b.
Step 3: Dissect one of the squares as shown below:
This dissection yields a square with side length a in one corner, a square with side length b in the opposite corner, and two rectangles, each cut along one diagonal into two right triangles.