Day 10: Special Segments and Triangle Inequality

We did an entire unit today. It started out with looking at midsegments and then we moved to perpendicular bisectors, angle bisectors, medians, altitudes, and all those fun centers that go along with the points of concurrency. I had done this awesome discovery activity when I student taught where it takes you through determining if the segments have a point of concurrency and all those equidistant things, but I couldn’t find it anymore. I searched for some ideas online but couldn’t find anything I liked that much. I didn’t think to email my old Geometry co-op until typing this out…maybe I can get it for next time. But we did go through what some of those relationships were and had fun drawing all the segments, using different colors and everything.

I also did a discovery activity for the inequalities in triangles. To see that the sum of two sides have to be better than the third, I had the kids use stick pretzels to test it. The only issue is that when they get to the one where the sum of two sides equals the third (which shouldn’t work) a lot of the kids don’t follow it close enough to make sure the two pretzels are really exactly the same size. Because of the error with that, a lot of times you have to go through that set again with students. I had some pasta sticks on hand for that purpose because it’s a little easier to see (but definitely not as fun to eat). Here’s the file:

I also had some kids turn in their Swan Challenge. It’s all about finding angle measured in this really complicated swan picture. Takes a lot of focus but it’s actually not too difficult once you get on a roll. Really more about perseverance. Here it is if anyone wants it:

Quelquefois, je pense de quelque chose un peu tard, mais c’est pas grave. Mes étudiants apprennent encore.

Day 8: Triangle Congruence

Our main activity today consisted of discovering the triangle congruence theorems and postulates. I used an activity (download below) where students had to construct 6 different triangles. Four of them can only form one triangle, two of them (AAA and SSA) don’t. I have students construct these in groups and then at the end I let them tape up their triangles on the board with all Triangle A’s together, Triangle B’s together, and so on. Students then do a gallery walk where they are asked to give what they notice about certain triangles. In the end, they see that SSS, SAS, ASA, and AAS gives us congruent triangles. One thing to note is that this take a long time. Even with groups of three and only six triangles, it took my class an hour to get them all done. Groups that finished early were asked to try to make different triangles with the same given information. But I think the time pays off in the end because the students can really see that AAA and SSA really don’t work and are pretty surprised that the others do.

 We then practiced a lot of proofs and got into CPCTC before they took a quiz on it. The quizzes were ok…not great…but this quiz usually is. I leave a lot of feedback on what could help them in their proofs and usually this helps them a lot. Hopefully they actually look at my feedback. I usually get some comment like, “Well I knew we had to use CPCTC in the proof during class because we just talked about CPCTC but then in the quiz all I could think of was No Choice Theorem.” No Choice Theorem?! You mean the thing we literally did one example with and then never touched on again? Ok…I’m still searching for the best way to help students with proofs in such a small time frame. I feel like during the regular year when this unit spans weeks, it would be easier for students to build up to their reasonings.

Les étudiants pensent que les preuves sont trop difficiles, mais il n’est que le début!