Cell 1 may be the most common proof to discuss with students. Would you do this at the start of a unit, in the middle, at the end, or not at all? Do you ask students to reproduce the proof? Do you think they remember it and does it matter if they don’t?
How and when might you introduce the proof in cells 2, 3 and 4? Are there any proofs you absolutely wouldn’t show? Is there a circumstance in which you would show this prompt, then take it away and ask students to reproduce it?
Cell 3 provides a more general result about similar triangles. Are there any other general results which reduce to Pythagoras?
Do you know any other proofs of Pythagoras? What’s your favourite proof of Pythagoras and why?