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Session 3, Part C:
Hidden Polygons
In This Part: Definitions | Understanding Definitions | Dividing Polygons into Triangles
Triangles in Convex Polygons
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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.
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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.
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Problem C4 | |
How would you divide the polygons below into triangles?
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