I ask students to look at their worksheet from yesterday and pick one acute triangle, one right triangle, and one obtuse triangle. I then call on 3 kids at random to share their side lengths.
I’ve gone through a great deal of discovery work yesterday, so it’s time for a little guided instruction. I give a small lecture about the Greeks, who were faced with a similar problem. Except the Greeks noticed something pretty cool that happens when you square the sides…
I square the sides for each triangle and ask students to look for patterns for 2 minutes. In each class, someone noticed that the right triangle’s short sides added up to the long side when all sides were squared.
So we use that as a springboard to analyze acute and obtuse triangles. Pretty quickly, we see that acute triangles’ short sides add to more than the longest side, whereas obtuse triangles’ short sides add to less than the long side. (I keep saying, over and over, “after you square all the sides” like a broken record because I am terrified of students forgetting that step.)
So now we have a hypothesis. How do we test it? Three new triangles! I get three new triangles from my students and try out our hypothesis, which seems to work!
Time for notes in our $1 Textbooks. We write down the Pythagorean Theorem, a diagram with the legs and hypotenuse defined and labeled, and the rule for classifying triangles using only their sides.
Finally, I give students a final triangle worksheet. In this worksheet, they are given the sides but not provided a ruler. They must use this new classification tool to classify the triangles.
If we have time, I’ve embedded an extension task in this worksheet. In the first problem, we had sides of 6, 8, and 11, which resulted in an obtuse triangle. The second problem, 6, 8, 8, resulted in an acute triangle. What would we need the hypotenuse to be to make a right triangle?