Exploring a Formula for the Sum of Interior Angles of an n-gon

Exploring quadrilaterals

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Reflection Questions:

 

  1. Explore each sketch to the left by moving the vertices around.  Check to see if the formula holds for all quadrilaterals, pentagons, and hexagons.

  1. In each case, explain why the formula seems to work.  HINT: Click on the "Show triangles" button.

  1. Can the formula be generalized to any n-gon? If so, what would that formula be?  NOTE: Assume that one can locate a point P inside the given n-gon such that all of the triangles are inside the polygon.

  1. Develop a sketch in GSP to test the formula for a convex octagon.

 

 

 
Exploring pentagons

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Exploring hexagons

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Sketch (c) JSB, Inc., 2006
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