# Assignment Five: GSP Script Library

By: Melissa Wilson

In Geometer's Sketchpad (GSP) it can be tedious to recreate simple constructions repeatedly. Below you will find a list of some common GSP constructions:

 Centroid of a Triangle The centroid is located at the intersection of the medians of each side. The orthocenter is located at the intersection of the altitudes of each side. The circumcenter is located at the intersection of the perpendicular bisectors of each side. The circumcircle has a center at the circumcenter and passes through each vertex of the triangle. Incenter is located at the intersection of the angle bisectors of the triangle. The incircle has a center at the incenter of the triangle. The radius of the incircle is the perpendicular distance from the incenter to each side. The medial triangle has vertices at the midpoint of each side. The orthic triangle's vertices are located at the foot of each altitude on each side of the original triangle. The vertices of this triangle are located at the midpoint of the segment that connects the orthocenter to each vertex of the original triangle. A pedal triangle is made by selecting a point P and creating the perpendiculars from each side to that point. The vertices of the pedal triangle are located where the created perpendiculars intersect each side. The center of the nine point circle is at the mid point of the segment formed by the orthocenter and the circumcenter (called Euler's Line). Circle formed for a given triangle using the following nine points: Midpoints of each side, the foot of each altitude, the midpoint of the segment from the orthocenter to each vertex. Takes a given line segment and splits it into three equal parts. Given a line segment, creates an equilateral triangle with the sides the length of the given segment. Given a line segment AB, creates a square with that segment as a side. Isosceles triangle, given base and altitude Given a base length and an altitude, creates an isosceles triangle. Given a triangle, finds the orthocenter (H), centroid (G), circumcenter (C), and incenter (I) Given a triangle, finds four centers of the triangle (H, G, C, I) and then also forms the Euler Line, which connects the orthocenter, centroid, and circumcenter. Divide a segment AB into two parts that form the golden ratio Given the segment, this script divides the segment into the golden ratio. Pentagon, given a side Given a side length, constructs a pentagon. Pentagon, given a radius Given a segment, constructs a pentagon with a radius of that length. Hexagon, given a side Given a side length, constructs a hexagon. Octagon, given a side Given a side length, constructs an octagon.