Session 3, Part C:
Hidden Polygons

In This Part: Definitions | Understanding Definitions | Dividing Polygons into Triangles
Triangles in Convex Polygons

 You may know that the sum of the angles in a triangle is 180°. Can you prove it? In Session 4, we'll look at one mathematical argument for which the result is true. For now, we'll assume that it's true (based on some strong evidence) and look at some consequences of that fact. This is how mathematicians often work: They assume an intermediate result, called a lemma. If the lemma turns out to be useful in proving other results, they go back and try to prove that the lemma itself is true.

 Video Segment Watch this video segment for a quick demonstration that shows that the sum of angles in a triangle is 180°. Even though this is not a proof, it will be useful for building further conjectures about polygons. If you are using a VCR, you can find this segment on the session video approximately 16 minutes and 28 seconds after the Annenberg Media logo.

 Problem C3 Polygons with any number of sides can be divided up into triangles. Here are a few examples: Draw several other examples of polygons divided into triangles for polygons of varying numbers of sides. Be sure not to use just regular polygons, and be sure not to use just convex polygons.

 Problem C4 How would you divide the polygons below into triangles?

 Problem C5 Describe a method so that, given any polygon, you are able to divide it into triangles.

Make sure your method works for regular and irregular polygons, and also for convex and concave polygons.    Close Tip

 Session 3: Index | Notes | Solutions | Video