Use the figure below to formulate a proof of the Pythagorean Theorem.[br][br]What assumptions do you make? Can you prove those assumptions?[br][br]Compare your proof and assumptions to Euclid's:[br][br][url=http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html]http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html[/url][br]

Move point A down to Point C so that you have a square. How is this square area constructed? [br][br]Now move Point A up. What relationships change and what relationships remain invariant?[br][br]Can you use such transformations to provide an argument for the Pythagorean Theorem?

What generalization of the Pythagorean Theorem is suggested by the applet shown below? [br][br]How would you formally state this generalization, and how would you prove it?