Polygon Interior Angle Sums
Play with the different animations, noting how changing the interior angle measures affects the sum of the interior angles. [br]As you go through create and complete a chart like the one below in your notes.[br]
After you have completed the table, what can you say about the sum of the measures of the interior angles of a polygon?
Diagonals in Polygons
Use the segment tool (first click on the line icon [icon]/images/ggb/toolbar/mode_join.png[/icon], then the segment icon [icon]/images/ggb/toolbar/mode_segment.png[/icon]) to draw the maximum number of triangles you can, inside the polygons. Only use the polygon’s vertices as points, such that no 2 diagonals overlap.
In your notebook record the number of triangles made inside each polygon. Create a chart like this one to help you.[br]
How does this second table relate to the first one? What connections can be made?
What is the sum of interior angles of a polygon with 9 sides? Explain your thinking.
Come up with a formula in the form of [math]S\left(n\right)=[/math] , where S is the sum of interior angles and n is the number of sides. Using your work with the diagonals and the table, explain why it works.