**Assignment 5 Write-up**: GSP Script Tools

**Chelsea Henderson **

Here, I will post the GSP Script Tools that I have created.

Centroid of a Triangle- The centroid of a triangle is the intersection of the three medians of the triangle. The centroid of a triangle is typically labeled with a G.

Orthocenter of a Triangle- The orthocenter is the intersection of the three perpendicular segments from one vertex to the opposite line segment. These perpendicular segments will be the altitudes of the triangle when they are inside the triangle. The orthocenter will not neccessarily be inside the triangle, so we cannot say it represents the intersection of the altitudes. The orthocenter of a triangle is typically designated with an H.

Circumcenter of a Triangle- The circumcenter is a point equidistant from each of the three vertices. The circumcenter of a triangle is constructed from the point of intersection of each side of the triangle's perpendicular bisector. The circumcenter of a triangle is labeled with a C.

Circumcircle of a Triangle - The circumcircle is the circle that inscribes the triangle. The circumcircle is constructed using the circumcenter as the center of the circle and any vertex of the triangle as a point on the circle.

Incenter of a Triangle-The incenter of a triangle is a point equidistant from each of the three sides of the triangle. The incenter is constructed from the point of intersection of each of the three angle bisectors. The incenter is labeled with an I.

Incircle of a Triangle- The incircle of a triangle is a circle inscribed in the triangle whose center is the incenter of the triangle. The incircle is constructed by first creating a perpendicular line from I, the incenter, to any of the three sides. A circle is formed from the point formed above on any side and the center I.

Medial Triangle- The medial triangle is the triangle formed by connecting the three medians of the sides of an original triangle. The medial triangle is similar to the original triangle and its area is one-fourth the area of the original triangle.

Mid-Segment Triangle- The mid-segment triangle is constructed using the orthocenter constructed above. The vertices of the mid-segment triangle are the midpoints of the segments from the vertices of the original triangle to the orthocenter.

Orthic Triangle- The orthic triangle is constructed from connecting the feet of the three altitudes of the circle.

Pedal Triangle- The pedal triangle is created by placing a point- the pedal point- anywhere on the plane and constructing the perpendicular lines from the point to the lines of a triangle. Connecting the three points of intersection of the perpendicular lines and the lines of the triangle creats the pedal triangle.

Nine Point Circle- The nine point circle is most easily formed by first creating the center from the midpoint of the segment connecting the orthocenter and the circumcenter and a point on the circle from any midpoint of a side of the circle. The nine points on the circle are the three midpoints of the sides, the three feet of the altitudes, and the three midpoints of the segments from the vertices to the orthocenter. See assignment 4 for a more complete description of forming the Nine Point Circle.

Center of the Nine Point Circle- This tool gives only the center of the nine point circle constructed above.

Trisection of a Line- Here is a tool that will give a line segment divided into three equal parts.

Equilateral Triangle- Here is a tool that will create an equilateral triangle, a triangle with three equal sides.

Square- This tool will construct a square given a segment.

Isosceles Triangle- This tool will construct an isosceles triangle, given the base and the altitude of the triangle.

Triangle Centers- The triangle centers are H- the Orthocenter, G- the Centroid, C- the Circumcenter, and I - the Incenter. See the specific construction descriptions of each center above. This tool will show and label all four centers for any given triangle.

Euler Line- The Euler line can be constructed for any non-equilateral triangle. The Euler line passes through the following centers of the triangle: Orthocenter (H), Circumcenter (C), Centroid (G), and the center of the Nine-Point Circle. The tool here shows the Euler line passing through the points.

Locus of vertex of a fixed angle that subtends a fixed segment. - This tool shows the locus of the vertex of an angle that subtends a segment.

Golden Ratio Segment- Here is a tool that will divide any line segment AB into two parts that form the golden ratio.

Pentagon, given a radius - This tool will produce a pentagon when the radius of the pentagon (the segment from the center to any vertex of the pentagon) is given.

Pentagon, given a side - This tool will construct a pentagon, given any side of the pentagon.

Hexagon, given a side- This tool will construct a hexagon, given any side of the hexagon.

Octagon, given a side- This tool will construct an octagon, given any side of the octagon.

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