The above figure contains a representation of a proof of the Pythagorean Theorem. If you can visualize the proof from the figure, then it is truly a proof without words. Such proofs have become somewhat popular; there are at least two books titled Proofs without Words by Nelson and Watkins.
I was not aware of this particular proof until I saw the figures on a course flyer; I did not immediately recognize that the figures represented a proof. Later that evening I had the Aha! moment. What struck me was how understandable this proof could be to a secondary geometry class of fifteen-year-old tenth graders. My experience as a secondary mathematics teacher made me painfully aware of the acute algebra deficiencies that burden these students; these deficiencies make an algebraic proof of the Pythagorean Theorem an exercise in frustration and futility.
While I doubt many students will be able to look at the figure and immediately experience an epiphany, I believe the figure can serve as a foundation to a brief pictorial demonstration of the proof of the theorem. Epiphanies are more likely to follow at this point. I believe this sequence can be a useful tool for secondary geometry teachers.
The pages indexed by the frame on the left show this development. The final link allows the reader to download a PowerPoint presentation of the pictorial proof. Teachers fortunate enough to have computer/AV classroom access are welcome to use the presentation.
Each content page contains a small printer icon
near the bottom of the page.
Clicking this icon will open a new window containing the proof content frame
but omitting the link frame on the left.
Interested readers may print the page from this new window.