Sunday, January 09, 2011


Is there a more fun thing that spills out of your mouth from geometry? I told my students that part of their homework was to repeat "CPCTC" 5,000 times correctly, and if they messed up, they had to start back at 1 (same for the whole phrase "corresponding parts of ...").

Anyway, this went well. I had them complete part of the following sheet in class JUST for proving the triangles congruent, so what three facts did they need to know and could they deduce from the picture to prove WHICH triangles congruent AND by what theorem/postulate. We did 1 together, then they did 2 on their own and we talked. Then 4 and 5 similarly (because they have special issues the kids come up against). I partly liked this sheet because it forced them to think about what they needed to use the theorems. They also messed up on #4 and claimed angle S congruent to angle S, so we had a discussion on naming conventions. They also messed up on #5 and put that angle W congruent to angle Y instead of claiming that the triangles were right. We discussed why the change/need and how ultimately you could just assume the triangles are right from the diagram.

Then I asked what extra things could they figure out BECAUSE they knew the triangles were congruent AND WHY. Then, in the white space on the right, we drew the 3 arrows from the triangle congruence statement to the 3 extra things we knew (flow proof style). They were fine with #1, and then some messed up with #2 because they were on autopilot and just put the 3 sets of angles were congruent (just like #1). We discussed how that's not NEW information and fixed it. Then I had them guess what reason we might claim. We finally got around to CPCTC. They finished the rest for homework.

Here's the sheet we worked on:


  1. I don't let my beginning students use CPCTC because they memorize it but have no clue what it means. I still remember my sister using CPCTC for every reason when she did proofs in high school.

    It is a fight because the kids that are repeating only want to use the short cut.

  2. Hmmmm, that's a good point. I'll have to make sure I assess their use of it frequently in the beginning, to make sure they know the full intent. Thanks.

  3. Pissed off you are so correct on that one.

    totally off subject Ms. Cookie, what chapter are you guys on? We are on chapter 8 and congruent triangles was in chapter 4. When do you get out of school?

  4. We're finishing up chapter 4 in Holt. I'm not really using the book as I have other resources. We spent a ton of time on logic, so that's probably why we're still on triangles.

    I'm a wee bit stressed about the time, but I've mapped out the rest of the year, and we can get to it all. AND we get out sometime EARLY June 3rd? 4th? What about you?

  5. we get out the same day. Our school likes to finish the book before the state testing which is in March.

    Yeah that's basically 2 months of nothing new to do because it's done for the state testing.

  6. Holy Cow! That's crazy! So you rush rush rush and then the kids twiddle their thumbs? What other crazy things are they going to make us do?

    So what DO you do for April and May? Fractals? Spherical Geometry? Tesselations?

  7. Anonymous12:08 AM

    I'm with P'ed O on CPCTC. We just don't use it. Teacher down the hall does. I never will. I will short cut it, after a few weeks, as "corresponding parts"

    Our New York year begins after labor day, and ends June 28th. And the kids are doing inequality proofs.


  8. we used to go back and hit things that weren't on the test, but the last couple of years we actually hit them hard on Algebra review to get them ready for Algebra 2.

    Some schools out here actually start the next book after state testing.

  9. jd2718: Aye, now I'm spoiled with the TX getting out at early June, so 6/28 sounds SO long.

    Mr. W: algebra review is a great idea, I know I'm trying to sprinkle it through geometry. One day I'm SURE they'll be able to manipulate ANY line problem I give them .... I just KNOW it .... one day .... soon ... yes ...

  10. This is beautifully done - so is your triangle congruence puzzle sheet. So stealing! Thank you for sharing them.

    I don't use CPCTC, either. They write (with abbreviations) "congruent triangles imply congruent corresponding parts." I try to make every "reason" a conditional statement, to help them see deductive argument of one thing leading to the next.

  11. Thanks, Kate, and you're welcome to them.

  12. Great post on CPCTC! I don't use it much either. found some good info on one of the posts from Math Teacher Life at posts.

  13. Mr. W: algebra evaluation is typically a superb idea, i understand I'm attempting to sprinkle it by method of geometry.
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  15. I'm trying to get through congruent triangles during this time of distance learning so I'm totally skipping 2-column proof. Don't hate me. 1/3 of the kids don't get it when I stand over them!, and there's no way I can find to see how they mark their diagrams for given information. Knowing them, they'll stare at the screen and write any old thing. So I'm looking for a way to get the concept of CPCTC across without doing the entire proof. This worksheet is perfect! It plants the seed of listing what we know to decide the triangles are congruent without starting with "B is the midpoint of..." Thank You!

    1. Anonymous1:45 PM

      Thanks, Patti! ..... Oh I miss teaching geometry, it's been forever and a week. Good luck with all this COVID distance crisis teaching.