Geometry Teachers---Triangle Congruence Constructions and Proofs

Discussion in 'General Education' started by RadiantBerg, Nov 30, 2013.

  1. RadiantBerg

    RadiantBerg Cohort

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    Nov 30, 2013

    We are starting the unit on triangle congruence proofs (SSS, SAS, HL, ASA, and AAS) and constructions soon.

    Last year I did all of the required constructions on the first day (I hate teaching constructions by the way, but it's a necessary evil with the Common Core), spent the second day on problems related to simply "recognizing" each case without writing a formal proof, and then 3 days of proofs.
    It was good, but not great.

    The other teachers do one of the cases each day (with only SSS and HL on the same day). They start with the construction and then proofs. I kind of like their set-up, but at the same time they only do one day with bringing all of the different theorems together since each day they are just focusing on one. I feel many kids struggle picking which to use, and this is why I introduce them all at once....but maybe it would be easier one day for each.

    What do you think, and how do you teach them? Introduce all at once, or spread them across different days?
     
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  3. Aliceacc

    Aliceacc Multitudinous

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    Dec 1, 2013

    We don't do constructions :) (Really, who thinks it's a good idea to give a sharp object to 15 year old boys???)

    But I do a day on SAS, then one on ASA and SSS, and a third on HL and AAS-- much of that day is on the difference between AAS and ASA. I also mention that there's no "donkey theorem" and that we'll talk about AAA when we do similar triangles but that it will NOT prove congruence.

    Then I go right to CPCTC and mix up all the methods of proving the triangles congruent.
     
  4. Shanoo

    Shanoo Habitué

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    Dec 1, 2013

    We do constructions using bullseye compasses. Not perfect, but better than the potential death-sticks that are regular compasses in the hands of 15 year old boys :)

    Last year, I introduced them all on the same day, and I don't feel like the kids got a true understanding. This year, I may spread it out.
     
  5. CindyBlue

    CindyBlue Cohort

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    Dec 1, 2013

    I teach the congruences over three days.
    I love teaching constructions, and the kids love doing them. I try to spend a week on constructions if I have the time. It so much fun for them to see that they can inscribe a circle, or circumscribe one, after just a few simple constructions. I apply constructions to making things, such as easily making a square corner with a string and a stick when you are building a carport.
     
  6. TeacherGroupie

    TeacherGroupie Moderator

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    Dec 1, 2013

    (Aw, Alice: the first time I did anything with constructions was in sixth grade, with the compasses that used golf pencils. We all thought that making and dividing lines and circles with lines and circles, using just a pencil, a compass, and a straightedge, was The Coolest Thing Ever. Not that we were doing actual proofs, to be sure.)
     
  7. mathteachertobe

    mathteachertobe Cohort

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    Dec 1, 2013

    I love doing and teaching constructions. I also used the bullseye compasses. The students really enjoyed them as well. I spent one day per triangle congruence, starting with the construction then working through the proof. I would think they would all get jumbled together otherwise. We also demonstrated ASS not working, with one student finding out, if the angle is obtuse, there's only one way to draw it.

    I'm only teaching Algebra this year, I really miss Geometry.
     
  8. Aliceacc

    Aliceacc Multitudinous

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    Dec 1, 2013

    Same here.
     
  9. Aliceacc

    Aliceacc Multitudinous

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    Dec 1, 2013

    When I cover SSA not working, if I have time, I show them the Ambiguous Case from the Law of Sines-- two triangles, with the same Side-Side-Angle, but where the 2nd angles are supplements.

    Definitely an "AHA!!"moment
     

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