## 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: