11/22/2014 26 Comments
Discovery: Congruent Triangles
They can thread one of each length onto a piece of yarn and tie it off to create a triangle. Challenge them to create a second triangle with the other three pieces that is NOT congruent to the first. (They discover SSS for themselves)
Next, use a paper clip to fix an angle between two straw lengths, and challenge them to again create another triangle. Continue the process, going on to ASA and SAS.
I like to have students record their observations by writing a conditional statement of their own explaining their discoveries for each pair of triangles. Give them only this structure as guidance: If ____________, then _______________.
After the hands-on investigation, have students share the rules that they wrote for congruent triangles. Clear up any misconceptions and give notes on notation, order of vertices, etc.
I talk about why AAA and SSA are not sufficient to prove triangles congruent. We also discuss HL and AAS. On a block schedule, this all can fit into one class period, but on a traditional schedule, it makes sense to break congruent triangles into a couple of days.
I like to set up practice afterward in a way that leads smoothly into proof writing.
I require them to write congruency statements, identify all the corresponding parts, and work with complex diagrams with two triangles, like they will see later on. This helps lead them into the next steps more easily. Here's my practice pack.
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1/2/2015 02:00:52 pm
Hey Math Giraffe!
1/2/2015 11:20:32 pm
8/5/2015 01:59:42 am
How do you use the paperclip to get a fixed angle for SAS? And AAS?
8/5/2015 11:10:40 am
Depending how much time you have, they can just bend to a matching fixed angle and tuck it inside. If you have time, it's best to have plenty of extra string, and actually tape string all along the angle of the paper clip to keep them attached. Then, when they "thread" the string through the two straws, they will be forced to keep that angle. Thanks so much for your question. Enjoy the activity!! :) My kids loved it.
1/16/2019 11:02:36 am
Hi. This activity looks like a great idea. I'm just struggling to figure out how to fix the angles. I don't really understand how the paper clips come into play. Do you have any videos/pictures/explanations that can help me? I'd like to try this lesson in a week or so.
9/16/2021 10:05:31 pm
I am having a hard time picturing what are describing. Do you have a photo or a video?
10/9/2015 01:37:25 pm
How do I get the instructions for this activity?
10/9/2015 02:51:08 pm
10/26/2015 07:25:10 am
1/4/2017 05:05:19 am
Thanks for this idea. I would try this one for my practice teaching. :D
1/10/2017 07:16:24 pm
1/13/2017 12:32:18 pm
9/28/2017 04:06:04 pm
Love this idea. Though i am little skeptical about how to formally deliver the instructions, still going to try it since I really like the idea plus I am becoming a bigger fan of enquiry based learning for my kids day by day.
9/30/2017 10:42:55 am
3/19/2018 01:28:03 pm
awesome lesson. Thank you.
7/25/2018 06:00:36 pm
Such a great activity - thanks so much.
9/12/2018 06:00:22 am
There are some interesting points in time in this article but I don?t know if I see all of them center to heart. There is some validity but I will take hold opinion until I look into it further. Good article , thanks and we want more! Added to FeedBurner as well
11/4/2018 11:07:16 am
I've used this lesson a few times, once was for a formal observation, admin loved it...best part, students learned.
11/5/2018 08:43:32 am
That is wonderful! Thank you so much for letting me know it worked well for you! :)
1/16/2019 07:22:46 pm
1/28/2019 08:07:04 pm
Hi Brigid, I'm getting stuck on this activity again. How did they demonstrate ASA? You can't exactly fix two angles at the ends of the side, if there aren't two other sides attached...
1/29/2019 10:53:17 am
10/23/2020 07:26:43 am
This is a really cool idea! I found that string/yarn and paper clips were difficult to use though. Pipe cleaners to connect the straws and "fix" angles worked a bit better for me.
10/23/2020 10:47:25 am
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