Here is what my classroom looked like after Geometry yesterday;

We launched on a exploration about triangle congruency. I told students I would give them three different measurements and they had to create the rest of the triangle, labeling everything. What I provided looked like this:

Before hand we talking about how side b needs to be opposite of angle B. Each construction was color coded.

Today, we finished up the last two (SAA and HL) and then students had a gallery walk where they observed and discussed which groups of triangles appeared to be congruent.

We came together as a class and talked about it a little more then looked over a few examples of how SSA falls short and other combinations as well.

All in all I believe this was time well spent. We haven’t proved HL or AAS but this was a good way for students to enter into the concept of triangle congruency.

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I wonder what the students take away about SSA from doing this exercise? The reason I ask is because, in my geometry class, I certainly learned that SSA didn’t imply congruence, but it was only much later that I realized a given SSA triple could determine 0, 1, or 2 congruence classes, depending on the values. In other words, I learned that SSA tells me nothing, but it actually is giving us a lot and may set up a proof by cases.

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Interesting. I only have one section of geometry, and every single student created triangle was congruent. I put a compass up to the provided lengths/angles and showed them how it could swing out and intersected the side and two points.

I am interested in how you would guide students through discovering the different congruence cases?

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Great post. Love the investigation. Jen Silverman has a contructive activity along similar lines with paper pipe fittings: http://www.jensilvermath.com/geometry/triangle-congruence-with-geogebra/. Could use tech or not. Keep up the writing, and the awesome teaching. We love it.

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Thanks for stopping by and sharing the link! It appreciate it!

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