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Proofs and Geometry


Woman teaching geometry, from Euclid's Elements.

Woman teaching geometry, from Euclid’s Elements. (Photo credit: Wikipedia)

In all my years of tutoring, I’ve noticed that most students prefer algebra over geometry or the other way around.  Even when I was in high school, I preferred algebra.  Geometry required more effort on my part, especially when it came time to learn proofs.  I earned my first (and last) “F” on a geometry math test that had geometric proofs.  Of course I worked diligently to pull my grade up by the end of the year.  But I will always remember that test, the teacher (Mrs. Yarbrough), and the feeling I had when I got my test back.

This followed me for a long time.  Throughout the years, I was asked to tutor students in geometry.  I always had an internal conversation that went something like this:

“Why me, can they get someone else?  There has to be someone who loves geometry.  Now I have to tutor proofs.  Proofs made me fail my geometry test in high school.  Maybe they already learned proofs.  Okay, I can do this.”

Then I would learn that the students needed help with proofs.  Go figure!!!  Eventually, this happened a few times and through tutoring my students, I finally learned, understood, and appreciated proofs.

When I was in high school I only had access to the teacher, my textbook, and the books at the library.  With today’s technology it’s easier to get help with almost any subject.  I wish the internet were as accessible then as it is now.

Here are a few internet sites and videos to help you with proofs:

Sparknotes         Extensive notes about geometric proofs

For Dummies     Tips for “Mastering the Formal Geometry Proof”

WyzAnt                Steps for writing two column proofs

Your Teacher    A video of an example of a two column proof

Khan Academy  A video explaining how to solve geometric proofs

So, why do we teach proofs in geometry classes?  Who thought geometric proofs were important enough to confound even the best math students?  Joshua N. Cooper of the University of South Carolina made a compelling argument about the importance of proofs in math classes.  Read his article before you tackle your first proof!  It may help you accept proofs.

I hope this is helpful.  If you have other ideas or resources to help with geometric proofs, please share them in the comments section!


Author: Math Education Concepts

I am a Co-founder of Excel Philly, Inc. (Math Corps Philadelphia). I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I have a passion for Mathematics Education, especially in urban communities.

3 thoughts on “Proofs and Geometry

  1. I have always preferred geometry over algebra. Configurations. Art. Dimensions. As a scriptwriter, this would make sense. For me Geometry is the visual arts of math.


  2. Yes, this makes absolute sense. I have found that most of my students who prefer geometry are usually more artistic (in expression). 🙂


  3. “Why me, can they get someone else? There has to be someone who loves geometry. Now I have to tutor proofs. Proofs made me fail my geometry test in high school. Maybe they already learned proofs. Okay, I can do this.”

    I am literally laughing out loud. I am a tutor and this post came up in a google search for geometry proofs as the SAME EXACT THOUGHTS were running through my head :). I’ve managed to tutor geometry and avoid proofs for a few years now, but I’m nervous every time. It’s time to buckle down and learn those suckers. THANK YOU for these resources, so helpful!

    Liked by 1 person

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