Polygon Investigations

Note: Students need a working knowlege of Geometers' Sketchpad to complete this excercise.

 

In Triangle Explorations you found that the sum of the angle measures of a triangle is 180 degrees. You can use this property to find the sum of the interior angles of a convex polygon

1. Triangles in Hexagons.

  1. Use Geometers' Sketchpad to construct a quadrilateral, a pentagon, and a hexagon.

  2. In each of these convex polygons, draw all diagonals from one vertex. Notice that this divides each polygon into triangular regions.

  3. Use Geometers' Sketchpad to measure the sum of the angles in each of your polygons. Use this information to fill out the chart below

B. Chart (Print a chart for each student)


Name

Polygon Investigations

Polygon Number of Sides,

n

 Number of Triangles

(n-2)

Sum of Measures of Interior Angles.
Triangle

3

1

1(180)=180 degrees
Quadrilateral


Pentagon


Hexagon


Heptagon


Octagon


Nonagon


Can you come up with a conjecture of a formula (in terms of n) of the sum of the measures of the interior angles of a convex n-gon? Hint-see column 4 of your table.