Lines of Symmetry for a Rectangle

There are two lines of symmetry for a non-square rectangle.
*Can you guess how the lines of symmetry were found?
If you "reflect" this polygon over the line of symmetry, what happens to the figure? Specifically, what happens to the vertices?
Why isn't there a line of reflection from the vertices?
If this figure was a square, would there be more lines of symmetry?

Christy Bredestege, August 5, 2008, Created with GeoGebra