Convex Poygons and Their Diagonals

This GeoGebra applet draws diagonals from one vertex to divide the convex polygon into triangles.
Color sliders Red, Green, and Blue can be adjusted to change the color of the polygon.

It should be noted that diagonals drawn from any vertex would divide the convex polygon into the same number of triangles.

1. Draw your own convex polygons and calculate the number of triangles each one of them could be divided into.

2. Calculate sum of the internal angles of each of the polygons.

3. Finally derive general formulas for

(i) Number of diagonals
(ii) Number of internal triangles
(iii) Sum of internal angles
(iv) Sum of external angles

Shared by Gonadman and modified by Prabir K. Chandra, 2 February 2014, Created with GeoGebra