Point in a Regular Pentagon
This applet that deals with a regular pentagon is an extension of two
earlier applets - "Point in an Equilateral Triangle" and "Point in a Square".
After exploring the earlier applets as well as this one, what can you say about sum of the distances from a point in the interior of the pentagon to each of the sides? Why is this true?
Under what circumstances can you form a new pentagon using the five distances to the sides?
Can a similar result be obtained for any regular polygon with an odd number of sides?
What about polygons with an even number of sides?