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The Pythagorean Theorem

Part 1: Mental Actions & Transformational Geometry

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 these mental actions/transformations to provide an argument for the Pythagorean Theorem?

Part 2: Euclidean Geometry

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