Angles of Polygons

Diagonal

A diagonal of a convex polygon is a segment that connects two nonconsecutive vertices.

Create all the diagonals that come from point A.

How many non overlapping triangles are made from the diagonals from a single vertex?

Exploration

In the applet above, construct all the possible diagonals from point A. 1) For the quadrilateral, how many non overlapping triangles can you make? 2) Create a pentagon. Create all possible diagonals from a single vertex. How many non overlapping triangles can you make? 3) Repeat question 2 for a hexagon, heptagon, and an octagon. What do you notice about the number of non overlapping triangles?

What algebraic expression can you use to relate the number of sides (n) to the number of non overlapping triangles in each polygon?

Sum of Interior Angles

Use the applet above. Use the geometry tool to measure each interior angle of the quadrilateral. What value do you get when you add the four angle measures together? --move the vertices to make a different convex quadrilateral. What do you notice about the sum of interior angles?

Use the applet above to create a pentagon. a) Measure each interior angle. b) Find the sum of interior angles. c) Repeat for a hexagon. A heptagon. An octagon What do you notice?

Sum of Interior Angles

Can you come up with an equation to find the sum of interior angles for any n-gon?