**Assignment 5**

**GSP Script Tools**

**by Margaret Trandel**

**I have created script tools for the geometric constructions below.
Simply click on the links below to open the individual GSP construction files.
You'll need GSP on your computer to participate in this activity.
After becoming familiar with the terms, try to create your own script tools.
I really enjoyed this assignment and I think you will too! **

Centroid:
**the point of concurrency of the medians of a triangle.**

Orthocenter:
**the point of concurrency of the altitudes of a triangle.**

Circumcircle:
**the unique circle which passes through each of a triangle's three vertices.**

Circumcenter:
**the center of a circumcircle.
It is also the intersection of the perpendicular bisectors of the sides of the circumcircle's triangle.**

Incenter:
**in a triangle, the point of concurrency of the angle bisectors.**

Incircle:
**the unique circle which is tangent to each of the triangle's three sides.**

Medial Triangle:
**the triangle formed by connecting the three medians of a triangle.**

Orthocenter, Mid-segment Triangle:
**the triangle formed by connecting the orthocenter H of a triangle to the halfway points between H and the vertices.
.**

Orthic Triangle:
**the triangle formed by connecting the three altitudes of a triangle.**

Pedal Triangle:
**given a point P inside a triangle the pedal triangle of P is the triangle whose polygon
vertices are the feet of the perpendiculars from P to the sides of the original triangle.**

Center of Nine Point Circle:
**the center of the circle described below - it turns out to be the midpoint between the
orthocenter and circumcenter of the 9 point circle's corresponding triangle.**

Nine Point Circle:
**named for the nine easily constructed points on the circle -start with a triangle -
the three feet of the altitudes, the three midpoints of the sides and the 3 euler points
(an Euler point is the midpoint between the orthocenter of a triangle and a vertex) are all
on the nine point circle.**

Trisecting a Line Segment:
**dividing a line segment into three congruent segments.**

Equilateral Triangle, Given a Side:
**a triangle with three equal sides.**

Square, Given a Side:
**a four sided polygon with congruent sides and four right angles.**

Isosceles Triangle, given base and altitude:
**a triangle with at least two congruent sides.**

Triangle Centers (H, G, C, and I):
**see orthocenter, centroid, circumcenter and incenter.**

Triangle Centers with Euler Line:
**the Euler Line triangle centers are circumcenter, centroid and orthocenter.**

Divide a segment AB into two parts that form a golden ratio:
**the golden ratio in a divided segment exists when the ratio of the length of the whole line
to the length of the longer segment = the ratio of the longer segment to the shorter segment.**

**Note: The constructions below are all of regular polygons.**

Pentagon, given a side:
**a five-sided polygon.**

Hexagon, given a side:
**a six-sided polygon.**

Octagon, given a side:
**an eight-sided polygon.**

Thanks for opening the above script tools! Please e-mail me if you'd like to share any gsp script tool files.