Geometry – Day 67 – Simplifying Square Roots & Special Right Triangles

Come for:

  1. A review of Algebra & square roots.
  2. An investigation of 30-60 and 45-45 right triangles.

Stay for:

  1. One really good classwork problem.


  1. None


Slide Deck

  1. Ohioan, Utahn, Wisconsinite, Michiganite, New Hampshirite;
  2. We’re throwing back here to the first right triangle we solved. At the time we left things at square root(80).
  3. Squaring is all about making pairs out of numbers. Square rooting is all about getting rid of pairs.
  4. So here’s the alternate answer. Sometimes it’s useful to preserve the square root information, as we’ll make clear in the next classwork segment.
  5. More problems.
  6. For #13, tell them you want them to give you both the answer AND the question. [N.B. If you check the Quicktime, you’ll know what I’m saying. All the problems are up with blanks for answers, but #13 has a blank for both question and answer. They’ll catch the answer pattern for 8-12, know the answer for 13 and then work backward to find the question. It’s great. I didn’t come up with it.
  7. Why are they special?
  8. The 30-60-90 is one half the equilateral triangle.
  9. If the small side is 7, what is the largest side? Then Pythagorize them to find the middle side. [N.B. e – I know “Pythagorize” isn’t a real word.]
  10. The 45-45-90 is one half a square.
  11. Again we’re Pythagorizing, but looking for a rule, a pattern.

Notes & Revisions:

  1. This was not the slamdunk I thought it would be. For next year, I’ll definitely slap some more examples up there, flash-card-style. (Give a triangle, one side and one unknown.)I specifically shied from the x, 2x, xrad3, formulaic approach, but by our second confusing day so many students were drawing little cookie cutter templates using the formula, I’ll probably teach it next year.Typically, I plan so much and so rigorously I’m unsurprised by the instructional outcomes. I have no choice but to chalk this one up as a loss.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.