A script is a pre-set geometrical algorithm. The given construction is done for you automatically. You just need to select the appropriate points required for the construction. For example, say we want to construct the centroid of a triangle. We enter GSP, open the script for the centroid, place 3 points for which to examine, and then play the script. Below is a list of links to GSP scripts:

The CENTROID (G) of a triangle is the common intersection of the three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side.

The ORTHOCENTER (H) of a triangle is the common intersection of the three lines containing the altitudes. An altitude is a perpendicular segment from a vertex to the line of the opposite side. (Note: the foot of the perpendicular may be on the extension of the side of the triangle.) It should be clear that H does not have to be on the segments that are the altitudes. Rather, H lies on the lines extended along the altitudes.

The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, C is on the perpendicular bisector of each side of the triangle. Note: C may be outside of the triangle.

The INCENTER (I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle.

Creation of an EQUILATERAL TRIANGLE ($).

Creation of a SQUARE, given ($).

TRISECTION of a line segment (#*).

Dividing a line segment into 4 CONGRUENT PIECES ($).

Dividing a line segment into 5 CONGRUENT PIECES (#*).

Note (#*): You must highlight 3 points in GSP. The second two points must comprise the line segment that you desire to trisect. The first one makes no difference to the trisecting.