Proving the Pythagorean Theorem

Do you know how Pythagoras really figured out his famous theorem? See if you can answer the questions below, by using applet and your understanding of the Pythagorean Theorem.
1. Using the sliders for the values of a and b, notice that a is one leg of the red triangle and b is the other leg of the red triangle. Also, what is similar about the green, blue, and orange triangle? 2. How do the measures of the measures of the legs relate to the purple squares? What do you notice about the area of the purple square FGJH in relation to the value of a? What do you notice about the area of purple square JKML in relation to the value of b? 3. What would happen if you added the area of square FGJH and JKML? 4. How could you then find the length of one of the sides of the larger purple square ABCD? 5. Measure segment AB to see if your conclusion was correct. 6. What does the Pythagorean Theorem state?