Geometry – Day 65 – Pythagorean Theorem

Come for:

  1. A better-than-expected investigation of the Pythagorean Theorem.

Stay for:

  1. Last day of Phobia Week!


  1. Lab packets.


Slide Deck

  1. Fear of crowds, eating, kissing/love, rabies, words
  2. Discuss here a little about Pythagoras, the Pythagoreans, their code of silence, punishable by death.
  3. For the investigation you pass out lots of squares — 1×1, 2×2, 3×3, on up to 15×15 — and have them build triangles out of the sides. They write down the areas of the three squares and whether the triangle formed is obtuse, acute, or right. The conclusions follow pretty quickly from there.
  4. Translating words to symbols.
  5. Next year match this slide with one showing the accurately measured triangles for reference. (i.e. “Ohhh, it was acute.”)

Notes & Revisions:

  1. See slide #10.
I'm Dan and this is my blog. I'm a former high school teacher, former graduate student, and current head of teaching at Desmos. More here.


  1. Independent George

    March 23, 2007 - 8:28 am

    I love it.

    The pythagorean theorem was my first encounter with proofs (and, incidentally, Grover Cleveland, but I digress). I remember not being able to really grasp it at first, but nevertheless being aware that we were on the cusp of something huge.

  2. George, I feel like every math class from Algebra through Precalculus exists (in part) to set up this awareness that we’re “on the cusp of something huge,” that some whisp of this concept transfers over to that one, that this can all be predicted somehow, and then calculus takes you over the cusp itself.

    There are certain kids, I’ve found, who are eager to find that waypoint, the kids who never ask “Why are we learning this?” even when they should. It’s easy to take them to the cusp. It’s the others who trouble me. I can only chip away at their resolve not to be impressed by any of this. Any ideas you have towards that end would be appreciated?

    And I’m happy to deal you a hit of nostalgia, Scott. First one’s free.

  3. I’m with George, proofs just don’t get much better than this. It’s one you can do without even understanding what constitutes a formal proof. It’s probably my second favorite, next to the proof of the existence of irrational numbers.

    I’ve been reading your work for some time and I love it, but if I had to put my finger on a favorite feature, it would be that you manage to work the concept of probability into almost every lesson. It’s a favorite topic of mine and I would argue the single most ubiquitous mathematical concept that we must face each and every day. Kudos!

  4. Tony, I’m not sure I deserve any credit for pushing my uncontrollable gambling addiction onto my kids, but I’m glad you think it’s useful. You ever see a way to work a wager into a lesson, I hope you’ll toss me a comment.

  5. Proof? Where is the proof? I must have missed something here, maybe the keynote –> powerpoint conversion swallowed it.

  6. Dan, I don’t teach math – I do tech support, but I would like to ask your permission to share these with some teachers and I would like to make clear if it is okay to use these in there classes.

  7. Oh, my word, yes. Everything here is re-usable, re-mixable, etc., without attribution. I’m tired of putting these hours in on lessons I only use once a year.

  8. Thanks a lot – I’m not comfortable using things found on the internet without permission and these are wonderful. I find myself learning from them and and I am math challenged. I wish you had them up here at the beginning of the year when my daughter was having trouble with proofs LOL

    Again, thanks