You can control a kig construction by means of a "pykig" python script, that can be executed with the command pykig.py. Here is a nice example (hexagons.kpy) you can try:

kigdocument.hideobjects()
def hexagons (c, v, n):
  hexagon = PolygonBCV (c, v, 6)
  if n <= 0:
    hexagon.show()
    for i in range(6): 
      PolygonSide (hexagon, i, True)
    return
  cnew = MidPoints (c, v)
  hexagons (cnew, v, n-1)
  for k in [2,4]:
    v1 = PolygonVertex (hexagon, k)
    cnew = MidPoints (c, v1)
    hexagons (cnew, v1, n-1)
hexagons (Point(0,0), Point(1,0), 5)

You can repeat the latest construction simply by pressing the key 'Z'; this comes in very handy if you need to construct a sequence of objects with the same construction, especially if there is no shortcut for that construction.

One of the most powerful tools in Kig are the menus that you can enter by right-clicking on an object, or on some empty space in the document. You can use them to give objects names, change their colors and line styles, and lots of other interesting things.

You can construct new points without using the menu or the toolbar, simply clicking somewhere on the Kig document with the middle mouse button.

Kig can open several file formats: its files (.kig files), KGeo files, KSeg files, and, partially, Dr. Geo and Cabri™ files.

Kig has more than 20 objects and 10 transformations with more than 80 constructions you can use in your documents: open the Objects menu to see them all.

You can use the selected objects to start the construction of an object which requires the selected objects as arguments. For example, if you have two points selected, you can choose Start->Circle by Three Points from the popup menu to start constructing a circle by three points.

Kig can extends its object set using external macros. You can find some interesting macros on the Kig website: http://edu.kde.org/kig.

If you have more than one object under the mouse, and you want to select any of them, you can click with the left mouse button, while holding the Shift key, to get a list of the objects under the mouse cursor which you can then select from.

When you construct a locus, you can click on it with the right mouse button and select cartesian equation to see its cartesian equation, whenever it is an algebraic curve of low degree.