Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 3, Part C:
Definitions and Proof

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

There are a few different methods that will work for dividing a polygon into triangles. One method is particularly convenient because, for polygons with the same number of sides, you get the same number of triangles. Here's an outline of the method for convex polygons (minor changes are necessary if you work with a concave polygon):

 • Pick any vertex to start. • Connect that vertex to every other vertex, except the two that are adjacent to it.

Problem C6

Use the method above or your own method, and fill in the table below. Remember that we are assuming that there are 180° in a triangle. When you click "Show Answers," the filled-in table will appear below the problem. Scroll down the page to see it.

Number of Sides of the Polygon

Number of Triangles Formed

Sum of the Angles in the Polygon

 3 1 180° 4 5 6 7 n

Number of Triangles Formed

Sum of the Angles in the Polygon

 1 180° 2 360° 3 540° 4 720° 5 900° n - 2 (n - 2) • 180°

 Problem C7 Write a convincing mathematical argument to explain why your result for the sum of the angles in an n-gon is correct. Note 5

 Video Segment In this video segment, the participants discuss how to determine the number of triangles that can be formed in a polygon and the sum of the angles in that polygon. Watch this video segment after you have completed Problem C7. What formula do the participants come up with to determine the sum of the angles in any polygon? If you are using a VCR, you can find this segment on the session video approximately 19 minutes and 32 seconds after the Annenberg Media logo.

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 Session 3: Index | Notes | Solutions | Video