The Pythagorean Theorem
Part 1: Euclid's Proof
Use the figure below to formulate a proof of the Pythagorean Theorem.
What assumptions do you make? Can you prove those assumptions?
Compare your proof and assumptions to Euclid's:
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
Part 2: Transformational Proof of the Pythagorean Theorem
Move point A down to Point C so that you have a square. How is this square area constructed?
Now move Point A up. What relationships change and what relationships remain invariant?
Can you use such transformations to provide an argument for the Pythagorean Theorem?
Part 3: Generalizing the Pythagorean Theorem
What generalization of the Pythagorean Theorem is suggested by the applet shown below?
How would you formally state this generalization, and how would you prove it?