Proofs of the Pythagorean Theorem

Here are some proofs of the Pythagorean Theorem. Click on the links and answer the questions below.

Proof 1
Proof 2
Proof 3

Proof 1
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.
Proof 2
4. How do you find the area of a parallelogram?
5. Move on of the sliders a very short way until the square becomes a parallelogram. How does the area of the parallelogram compare to the area of the square it came from?
6. Move the slider a little farther until the parallelogram becomes a rectangle. How does the area of the rectangle compare to that of the parallelogram? How does it compare to the square?
7. When both sliders are moved, what happens? What does it show?
Proof 3
8. If the legs of this triangle have lengths a and b, what is the area of the red square? The blue square? Does it matter which is which?
9. Slowly move the slider to the other end. What is the area of the new shape? Write the area in two different ways.