Proof by Shear Transformation
Explore the proof of the Pythagorean Theorem by shear transformation. First, grab and drag point K as far down as you can. Compare the area of the red square and red parallelogram. Next, grab and drag point L to the left as far as you can. Again, compare the area of the blue square and the area of the blue parallelogram. Next, grab and drag point M towards point C. What can you say about the area of the green polygon compared to the area of the green square? How does the area of the green polygon compare to the areas of the red and blue parallelograms? To verify your conjecture grab point T to overlap these shapes.