Introducing Geometry Proofs

3/10/2015 21 Comments

Introducing Two-Column Geometry Proofs: A Different Approach

This post has been updated. Read it here, and get all the goodies to print and use in your own Geometry classroom:
How To Teach Geometry Proofs: A Better Way to Sequence Your Two-Column Proof Unit

21 Comments

Linda Mitcham

6/22/2015 04:03:32 am

DocRunning link

4/19/2016 10:45:13 pm

Thank you for this great post. I am teaching geometry (which I despised as a student) for the first time, and I appreciate the insights. Can't wait to try this.

Math Giraffe link

4/20/2016 02:29:06 pm

Hey Doc! :)
Im so glad you can use this. It makes a world of difference. I hope you love teaching geometry more than you enjoyed taking it! Good luck!
Thanks so much for commenting. :)
-Brigid

Charles Vochatzer

5/25/2017 08:46:40 pm

I too did not like (despised might work) Geometry in HS. Now, next school year (2017-18) I get to teach it. Yeah! I'll be looking into getting lots of help with this.

Math Giraffe link

5/28/2017 04:53:22 pm

Hi Charles,
I hope you learn to love it this time around! :)
Hopefully some of the resources here will help as you get started! Best of luck - let me know how I can help.
-Brigid

Terri

8/5/2017 05:23:11 pm

Also first year teaching geo in a long time with new text at a new school, ao looking forward to sharing and learning best practices!

Math Giraffe link

8/7/2017 02:52:08 pm

Hi Terri,
That is so great! I really appreciate hearing that you can use some of this :) Enjoy the Geometry! I hope you love it.
Have an awesome school year!
-Brigid

Marilyn McArthur

8/7/2018 11:50:29 am

Great ideas. I for the most part have the same students for Algebra I and Geometry - so do try to "prep" them with algebraic proofs during Algebra course. One thing I do require when doing proofs is have also number justification - to correspond with statement. When not using templates they often are hard to match up.

Becky Z

10/18/2018 09:48:44 pm

I have taught Geometry for the past 3 years, and started my career teaching Geometry from 1996 - 2003; so I am a veteran of the subject but still change up my technique every year that I teach it. This subtle interlude into proof writing is so clever, and something I haven't tried - I thank you and look forward to doing this lesson before simple Geometry proofs.

Math Giraffe link

10/22/2018 11:03:14 am

Hi Becky,
I hope that it works well for your students! It made such a difference for mine.
Thanks for commenting! Have an awesome week :)
-Brigid

Rebecca

2/12/2019 01:28:46 pm

Using substitution and transitive properties with the algebraic proofs makes so much sense when outlined above. Here's something I can never quite do a good job of explaining. The difference between when to use transitive and when to use substitution. Is one inclusive of the other? Meaning, any transitive property could also be considered substitution property? But not every substitution property is transitive? For example, in the proof just before Try It, could yo have used Substitution based on lines 3 and 5? THanks!

Math Giraffe link

2/12/2019 02:42:05 pm

Hi Rebecca,
Yes, thanks so much! This is a challenge, but I wrote up a post about this exact question :)
Here is that link - https://www.mathgiraffe.com/blog/teaching-substitution-vs-the-transitive-property
Hopefully that will help :) Have a great evening,
-Brigid

Chris Beggs

4/19/2019 09:54:33 pm

I agree with your "pet peeve" - I regard it as a "category error", segment AB is in the Geometry category, measure of segment AB is in the Arithmetic (or even Algebra) category.

I went through a longer list of what you can do: Segments: Congruent, can be parallel, can be perpendicular, can intersect, can be collinear ... Measures: Equal, can add, subtract, multiply, divide, cube, square root...

Then I emphasised that the "road" between the two categories is the definition of congruence - you can turn congruence into equality or vice versa; the segment addition principle is the "bridge" between them - it lives in both worlds.

Similar things then follow for angles and angle measures. Angles can be vertical, a linear pair, supplementary, complementary, alternate interior, ... but numbers can't be vertical etc.

For me, the more things in the lists, the clearer it becomes to the students as to what beongs in which "world".

Math Giraffe link

4/25/2019 12:11:01 pm

Hi Chris,
That is even better! Sounds really great.
I love those additions. Thank you so much for taking the time to share! :)
Have a great day,
-Brigid

Vicky

10/2/2019 11:52:27 pm

I am trying to download the Proofs Posters guide, but it will not send it to me because I already subscribe to your website. Is there anyway that you can resend those to me?

Math Giraffe link

10/3/2019 10:22:29 am

Hi Vicky,
No problem! Just send an email to [email protected] and I'll send them over ;)
Have a great day!
-Brigid

Kal C

5/24/2020 05:44:09 pm

Thanks for this. The style of proofs should be as logical as the proof itself. So I agree with your two-column poem structure, which is a systematic way to write a proof. It is essentially the same way that professional mathematics write their proofs, except in prose not in poem.

Just my one issue is in the way you have written the proof in your example. A proof is like a staircase. Your legs should move up the staircase one logical step at a time. So you start with: m = as the bottom step, and: = 3h is the top step. You climb up the staircase of the proof by filling in the steps in between one at a time. So I would structure it like this:

Given #1: g = 2h
Given #2: g + h = k
Given #3: k = m

Step #1: Start with: m =
Step #2: = k, using Given #3
Step #3: = g+h, using Given #2
Step #4: = (2h) + h, using Given #1
Step #5: = 3h, using transitivity

We started at the first step: m =, and ended at last step: = 3h. So m=3h, and the proof is done.

However, in your proof, you start at an intermediate step, which is like jumping steps or splitting your legs between two different steps.

This is just my two cents. Overall the article is appreciated. Thanks.

Kal C

5/24/2020 05:52:43 pm

Sorry, for Step #5, disregard "using transitivity". That does not apply there.

Math Giraffe link

5/30/2020 02:31:44 pm

Hi,
Thanks so much for chiming in! Yes, I think you are right - I appreciate your comment. :)
Thank you and have a great weekend!
-Brigid

Brandon

1/21/2021 09:47:31 am

Is there, or do you have a complete curriculum for Geometry? I do not like the textbook style which is the typical format.

Math Giraffe link

1/23/2021 11:24:49 am

Hi Brandon,
I don't have a full curriculum yet, but I do have a large set of resources, and the proof content in there is very comprehensive and will take your students all the way through the process of learning to write a proof with this method. It's very heavy on the proof and logic, but is not a full curriculum. The preview file here will give a look at what is included: https://www.teacherspayteachers.com/Product/High-School-Geometry-Super-Bundle-1948872
But then let me know what other questions you may have. Thanks, and have a great weekend,
-Brigid

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Introducing Two-Column Geometry Proofs: A Different Approach

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