Two different pentagram constructions. Use the Pentagram tools to make more stars.

The pentagrams above are examples of constructions. By dragging the points you can change the shapes, but however you drag the points, they are always pentagrams. They pass the dragging test. The objects you can see, depend on objects that you can not see.

Free and dependent objects

  • Make a circle icon
  • Make a point on the circle
  • Make a point not on the circle
  • Move all points

You can move the point D freely. If you move A or B you change the circle, these points define the circle. The points A and B are free but the circle is a dependent object, it depends on the points.

If you move C it moves along the circle. C is defined to be a point on the circle and is hence dependent.

Observe the algebra view; the point C and the circle c are dependent objects.

Construction protocol

Choose Construction Protocol under the View-menu. In the construction protocol you can see in what order the objects have been placed. The dependent objects are defined using other objects, their definitions are shown. You can change the order of some lines in the protocol but not all. Why not?




You can make a general polygon by using the tool Polygon icon. The last vertex of your polygon should be the point you started with.

When using the tool Regular Polygon icon, you make two points and then specify the number of vertices. Note that you don't have to create two new points, you can use existing points. Se the picture to the right.

There is no tool for creating a pentagram but you can make one by doing a construction.

Exercise - Construct a pentagram

  • Make a pentagon (a regular polygon with five sides).
  • Make segments between vertices of the pentagon by using the tool Segment between Two Points icon.
  • If you want to colour an area you must turn it into a polygon. The intersection points of the segments must be used as the vertices of the new polygon. There is a special tool for making an intersection point, Intersect Two Objects icon. If there are only two intersecting segments, the regular tool New Point icon will make an intersection point if clicked at the intersection. Create the five intersection points!
  • Use the tool Polygon icon to create the pentagram.
  • Hide the original pentagon by right-clicking on it and uncheck Show Object. Note that you can not delete the pentagon, it is used in the construction, you can only hide it.
  • Now you should be able to move the pentagram and change its size by dragging the points A and B; the dragging should not destroy the pentagram. It is this feature that makes it a construction rather than a drawing.

If you want make pentagram tools, as in the topmost applet, see GeoGebra Tutorial - Tools.

Intersection between several objects

Sometimes you want an intersection point where several objects intersect.


If you, as in the picture, have three segments intersecting at approximately the same point, don't click on the intersection of the segments but click twice, first on one segments and then on the other using the Intersect Two Objects icon tool. You can click on the segments either in the graphics view or the algebra view. You can only make an intersection between two objects.

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License