Triangle Sum Theorem Proof

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Objective

SWBAT use their observations to deduce the Triangle Sum Theorem.

Big Idea

When given the opportunity to connect their knowledge about lines and angles, students can deduce an important theorem.

Paper Corners Review

15 minutes

I created this lesson as an alternate approach to proving triangle angle sums. I find that many students are already familiar with the activity in which they cut off the angles and line them up to form a straight line. So instead of repeating the experiment, I start by reviewing some homework problems and  then I show the class this clear although somewhat bizarre video:

Source:  http://youtu.be/BQsO4WxAVb8

After the video I start a discussion around the concept of proof, "Could we use this experiment to show that this works for every type of triangle? Would that be possible?"

Here I want students to deduce that we need a better way to approach the problem. With a proof that looks at specific cases, we will never be able to prove that it always works for every case of a triangle, since we can always make a new case slightly different from the one before. I conclude by announcing, "Today you are going to prove that all triangles have 180 degrees. And you are going to do it without cutting up any triangles."

The Geogebra Module

20 minutes

I have created a Geogebra Module for my students that represents a basic variation of the triangle sum proof: 

http://www.geogebratube.org/student/m80592

My goal for my students is that they can build on our work from yesterday's class to create a proof of the Triangle Angle Sum theorem. The demonstration in the module by encourages students to use what they already know about alternate interior and supplementary angles.

I give them Module 6 Guide as a source of prompts to guide their exploration. A key to supporting the success of this lesson is to allow students to find the words that describe the angle relationship and support the writing of a proof.

Summary and Extension

25 minutes

In this part of the lesson, we ask several students to share their versions of their Triangle Angle Sum proof. I will show show the Powerpoint slides (Transversals) that include the Geogebra module again to spark conversation. I will ask students to volunteer to present their findings. I like to quote students when they have written particularly effective arguments. I will often put several proofs on the board during this lesson.

At this point many students still use specific number cases to make their argument, but I challenge them to think about the different between using specific angle measurements and variable angle measurements. 

We finish today with about 10 minutes on these extension problems:

Module 7

Before departing, we review students' answers and discuss the meaning of having similar or congruent triangles (these words appear in the last problem).