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11/22/2014 26 Comments

Discovery: Congruent Triangles

Discovering Congruent Triangles - SSS, SAS, and ASA
My big teaching passion is Geometry, and I absolutely love to use inquiry-based learning.

Geometry is just meant to be explored and discovered in a hands-on way!

Try this investigation with your class and allow them to discover SSS, SAS, and ASA for themselves.  They will really understand and remember it!


Materials:
(for each student or pair working together)
- 2 pieces of plastic straw 4 inches long
- 2 pieces in another color that are 5 inches long
- 2 pieces in a third color that are 6 inches long
- string or yarn
- 4 paper clips



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)
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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.

Congruent Triangles
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Congruent Triangles Practice that Leads into Proof Writing
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To Read Next:

26 Comments
Kacie Travis link
1/2/2015 02:00:52 pm

Hey Math Giraffe!

I LOVE this inquiry lesson! This is my first year teaching HS Geometry and I think this will be really helpful! Thanks for this post!

Kacie

Reply
Math Giraffe link
1/2/2015 11:20:32 pm

Thanks, Kacie!
I hope your students love it. Thanks for stopping by :)
I've been enjoying your blog too - love all the pictures!!
Happy New Year!
Brigid

Reply
Rachel
8/5/2015 01:59:42 am

How do you use the paperclip to get a fixed angle for SAS? And AAS?

Reply
Math Giraffe link
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.
-Brigid

Reply
Rivka
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.

Thanks!

-Jon
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?

Pam S
10/9/2015 01:37:25 pm

How do I get the instructions for this activity?

Reply
Math Giraffe link
10/9/2015 02:51:08 pm

Hi Pam,
This is the only instruction write-up I have done. Hopefully in the future will have more time to write it more officially. I had my classes do this one as a pretty informal investigation.
-Brigid

Reply
Teresa link
10/25/2015 10:18:08 am

There are angle manipulatives called AngLegs that easily snap together that can be used for this activity too! They are not too expensive.

Reply
Math Giraffe link
10/26/2015 07:25:10 am

Thanks, Teresa,
I just checked those out... very cool!! Thanks for sharing :)
-Brigid

Reply
Hazel
1/4/2017 05:05:19 am

Thanks for this idea. I would try this one for my practice teaching. :D

Reply
A
1/10/2017 07:16:24 pm

Hi,

How much prep time does this typically take, and how long does the inquiry part take for the students to do?

Reply
Math Giraffe link
1/13/2017 12:32:18 pm

Hi,
The prep only took me a few minutes. I trimmed the straws in sets and only did one set per pair of students. The activity took them only about 15 minutes because I did this as a pretty quick, informal one and they just jotted down the "If, ...then... statements." Sometimes for inquiry activities, I have students formally write up extensive observations, etc. and then it takes longer. Thanks!
-Brigid

Reply
Ayisha Shahani
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.

Reply
Math Giraffe link
9/30/2017 10:42:55 am

Hi Ayisha,
I hope your students enjoy it! The inquiry approach can make such an impact, especially in Geometry. Thanks so much!
-Brigid

Reply
bushra link
10/4/2017 12:05:35 pm

Good

Reply
Sonia
3/19/2018 01:28:03 pm

awesome lesson. Thank you.

Reply
Neil Marshall
7/25/2018 06:00:36 pm

Such a great activity - thanks so much.

Reply
mustafagameapk.info link
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

Reply
Tticia
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.

Thank you.

Reply
Math Giraffe link
11/5/2018 08:43:32 am

That is wonderful! Thank you so much for letting me know it worked well for you! :)
I'm so glad to hear it. Have an awesome week! Thanks,
-Brigid

Reply
Math Giraffe link
1/16/2019 07:22:46 pm

Hi Rivka,
The paper clips are just to bend so that the straws are supported held at a fixed angle. So after bending the paper clip to create an angle, the students slips a straw piece over each end. The pieces meet at the vertex of the paper clip. It only holds it loosely. There are better tools for this for sale now (this is an old post! -- sorry!) But this free version still works ok :) 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.
-Brigid

Reply
Rivka Boord
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...

I'm nervous about how to explain it to my students. I'm afraid that it's going to flop. Do you have step-by-step directions of some sort?

Reply
Math Giraffe link
1/29/2019 10:53:17 am

Hi Rivka,
We just did this in my class as a super low-key casual investigation. So we did not even do it for each shortcut rule.
The point was just to explore a bit and notice, and then we fairly quickly transitioned into whole group discussion about it, and then I started the lecture and showed them the shortcuts they noticed as well as introduced the other ones. I am sorry I don't have a full detailed lesson plan on this one. And to "fix" those, they just held them in place. It does not have to be perfect, but if your students are younger or not used to this type of thing, then you may want to write up directions, or choose to purchase the tools that are better for this that are now available. I believe they are called anglegs. Thanks! Have a great day!
-Brigid

Reply
Mike
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.

Reply
Math Giraffe link
10/23/2020 10:47:25 am

Hi Mike,
Yes! Genius. The paper clips were not ideal. I love the idea of pipe cleaners - so much smarter!
Thank you so much for sharing this. Have a great weekend,
-Brigid

Reply



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