Wednesday, November 24, 2010

Proving Triangles Congruent

We just started talking about congruent triangles in geometry. After a day of notation and vocabulary and such, I start up the class with asking them how many pieces of information a triangle has (6). Then I ask a series of questions: what if I asked everyone in here to draw a triangle. Is there a 100% probability that everyone would draw the same triangle? What if I told you one side had to be 5 cm? What if I told you that one side had to be 6 cm and one angle 40 degrees? And so on. Then they conjecture what would be the minimum amount I'd need to tell them. I get a range of answers, which is great.

Then we went through a series of carefully thought out constructions on my part of the 6 possibilities (AAA, SSS, ASS, SAS, ASA, AAS in order). I like that it gives them practice with protractors and compasses. There's also time for them to process (through the drawing), why some information doesn't give a unique triangle. We discuss how we know I gave them all the possibilities.

Then we barely had time (in a block class) for this side of the sheet:



In the past, students have had a hard time "reading the triangle information" in the right order. I think I found a fix. I have them lightly circle the sides or angles without information. Then I tell them that when they read the given information in order, they can't pass by 2 or more pieces of non-information. This seemed to help.

I assigned this side for homework:

2 comments:

  1. I like this. You said that this was not the first day of congruency. What was the first day like? What did the students bring to this lesson in terms of vocabulary and experience with protractors/creating shapes.

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  2. On the first day, we just discussed the notation of congruency: "if triangle ABC is congruent to triangle DEF, then that means, A corresponds to D and B to E, etc.". We'd also revisited working with protractors and such.

    Then on this particular day, I was very bossy about the triangles they'd make. For each set, we constructed them, and then I had them compare papers against the light to see if they were identical.

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