Working with triangle congruence

Today, we started by reviewing what we had learned so far about triangle congruence. I listed out SSS, SAS, and SSA and indicated which worked and which didn't. I then said the focus so far had been on looking at triangle sides. What happens when you focus on angles instead.

I wrote out the three equivalent statements for angles: AAA, ASA, and AAS. I felt this laid out some symmetry to the situation that would help students better relate to why we would investigate these options. I gave students some time to try these.

I walked around to see how things were progressing. There was the usual help with how to use a protractor but I was also amazed at how many students would just guess rather than try drawing the figures need. I asked how they came to their conclusion and the said they just guessed. What was the basis for the guess? It just looks like it wouldn't or would work. How can you know without having any foundation for your guess?

I encourage students to actually draw out their figures and measure their angles and sides. If nothing else, maybe they'll get better at using a protractor. The classroom discussion that resulted was mixed since there were still a decent number of students who just thought about it to draw a conclusion. We finally did get out that ASA and AAS worked but that AAA did not work.

We then practiced working through some congruence problems and a congruence proof. The proof gave the statements and students were to justify the statements with a reason. There was still a lot of struggle with the reasons although I am seeing some improvement.

The last two steps of the proof involve using a vertical pair and one of the triangle congruence theorems. Students didn't know what the name for the vertical pair was and couldn't articulate that because the angles were a vertical pair they were congruent. It's really difficult to write or complete proofs if you don't know that vocabulary and the properties of things.

Since no one seemed to remember or have this in their notes, the homework for tonight is to find out what the name of angles are when they are formed by two intersecting lines. They are also to identify the properties of these angle.