New to me this year, is teaching the Triangle Congruency Postulates (Theorems? Which is it?). You know the ones. SSS, SAS, AAS, ASA, HL? So, my first attempt didn’t go over so well, trying to use spaghetti. Fun, but it really only worked for SSS. Without angles, it ended there. (We did make some cool similar triangles, so that was a bonus!) So I needed a new plan. I’m pretty good at coming up with big ideas, but pretty poor at finalizing the details. I reached out to my Twitter world, and got some suggestion, but didn’t have time to look into them. Here’s what I ended up with. I made it a partner challenge.

Triangle Challenge: Can you Make A Different Triangle than Your Partner?

I gave each student a set of triangle parts. I made sure that no two students sitting next to each other had the same color straw. The box I bought had red, yellow, blue and green. I included some “angles” and some “sides.” I just cut the bendy part out of the straw leaving about a cm on each side.

The first direction was: Using 3 sides and 3 angles, make any triangle you want. You may cut the sides to make them shorter if you like. They could probably also fit straight pieces together to make longer sides too, but I didn’t try that. (It is really important that they use 3 separate angles and 3 separate sides.) Then trace your triangle on the worksheet. (I haven’t typed this up yet, so will post that soon.)

Next, take 3 parts of your triangle off and label them on your drawing. (This picture shows 2 angles and a side: ASA) Then give them to someone who has a different color straw.

Once you have received pieces from another person, the challenge is to NOT make the same triangle as they did. Here are the rules. You must keep the angles and sides they gave you the same and in the same places! Use their drawing to help you remember what they gave you and where the piece were. Use your extra pieces to make the rest of the triangle. Could you make a different one?

The goal of the activity is this: Depending on what combination of parts you were given you will or will not be able to make a different triangle. For example, if someone gave you all 3 sides, you could NOT make a different triangle. Therefore, 3 sides (SSS) guarantees congruence. If you were given 2 angles and 1 side in the ASA order or the AAS order, you could NOT make a different triangle, proving that ASA and AAS guarantees congruence. The students already understood the HL postulate, and no one made a right triangle, so I didn’t worry about it in this activity.

Now, of course, the sassier students will argue that they can make triangles that aren’t *exactly* the same. And that’s probably true because they’re just straws! It’s not a perfect material. However, for 8th grade, it was convincing enough. The other problem was that students only gave each other the ASA or SAS combination, so they rest came from me. The other problem is that the partner can move the angles if they are being sneaky, but even bendy straws stay pretty well in place.

So, overall, I think it was a success! The students definitely now have an activity to refer back to and it made the postulates (or are they theorems?) concrete and understandable. I’m putting together the worksheet soon, but plan on using this again next year! I would recommend cutting the straws apart ahead of time. I planned on doing this, but due to a late night (cough-2 year old not sleeping-cough), I did not get to do this. My first class however, was helpful, but the cutting out the angle was way harder for them than I thought. They got way too caught up in how far away from the bendy part to cut.

So, please comment, share your thoughts, ask questions. See any glaring inaccuracies or misconceptions, please let me know. This is the first activity like this that I’ve done that actually worked the way I wanted to! It’s about time! Or, if you’ve done this before and I totally stole it from you I apologize. I promise it was not on purpose and really just came from my brain. But great minds think alike, right?

I’m glad it worked! I never would have thought to use the bends as angles. Did any of your students show that ASS doesn’t work? I’ve never gotten kids to independently discover that there is both an acute and an obtuse option when given two sides and an angle not between them.

Nope. No one tried ASS on their own. It did come up later as we were talking more abstractly and they were able to reason why it wouldn’t work. I had students draw some on the board that wouldn’t be congruent. After some middle school giggles of course! I think next year, if time allows, I would have them try more combinations to hopefully get to all of the possibilities.