For this write-up there is a useful list of scripts attached to this link that can be accessed and used for other projects or within the classroom. To find the link to a specific script you might find useful, just click on the name of the scrpit you would like to see. A small picture and discription is next to each link. If you would like to add the tool to your personal toolbox, you can, however it will not automatically be there. You must have GSP to look at the links.
1. Centroid (G)
The centroid of a triangle is the intersection of the segments that connect the midpoint of one side to the opposite vertex.
The orthocenter of a triangle is the intersection of the perpindicular lines that are formed from a vertex to the opposite side of the triangle
The circumcenter of a triangle is the intersection of the midpoints of the triangles perpindicular lines to the actual line the midpoint lies on.
4. Circumcircle
The circumcircle is the circle that is connected by the three vertices of the triangle and has a center at point C.
5. Incenter (I)
The incenter is the intersection of the three angle bisectors
6. Incircle
The incircle is formed by creating the perpindicular lines from point I to each of the sides of the triangle. Selecting on of the points from the perpindicular lines and the edge and the center I will give a circle that is always inside the triangle
The Medial triangle is the triangle that is connected by the midpoints of the larger triangle.
8. Orthocenter, Mid-Segment triangle
The Mid-Segment Triangle is the triangle that connects the midpoints of the segments, from the orthocenter to the vertices.
The orthic triangle is the triangle that is connected by the intersections of the vertices to the opposite segment
10. Pedal Triangle
The pedal triangle is the triangle that is formed from the intersections of the perpindular lines forms from the given point to the extention lines of the original triangle
11. Center of Nine Point Circle
The center of the nine point circle is the midpoint of Euler's line. Eulers line is the line that connects the orthocenter (H), the circumcenter (C), and the centroid (G).
The nine point circle is constructed using the nine point circle center and three of the triangles discussed above. The medial triangle (organge dotted), the orthic triangle (green dotted), and the mid-segment triangle (yellow dotted). The points G, C, and H are taken out of this picture below do to adding confusion of more letters.
To trisect a line, draw a segmemt. Then get the midpoint and the midpoints of those points (quarters). Draw to circles using the endpoints as the centers with the radius the length of the orginal segment. Then draw two more circles using the radius as three-quarters of the orginal segment. Where these two circles intersect, draw perpindicular lines and where they intersect the original segment will divide them into three equal segments.
14. Equilateral Triangle, given a side
To construct an equilateral triangle, given one side-two circle with the sides length must be drawn. Then from there where the two circles intersect is the third point of the triangle
To construct a square given on side, the first step is to draw two perpindiculars from the endpoints. Then draw two circles that have a radius of the segment. After that draw the intersections of each circle with the perpindiculars. These are the other two points of the square. Then draw the segment connecting them, and you have a square.
16. Isosceles Triangle, given base and altitude
To construct an isosceles triangle you already know the base and the altitude (which must be perpindicular to the base). Extend the perpindicular of the line and connect the base points to the altitude point. Then the sides will always be equal.
17. Triangle Centers (H, G, C, and I)
A triangle can be drawn that has the four triangle centers appear and the centers H, G, and C are on a line, and I, G, and C form a triangle
18. Triangle Centers with Euler Line
Euler's line is the centroid, orthocenter, and circumcenter of a triangle
19. Divide a Segment AB into Two Parts that form a Golden Ratio
To divide a segment into the golden ratio you must first draw the segment. Then find the midpoint. Connect the midpoint to one of the points and make a circle. Then you draw a perpindicular from the point you picked and connect the intersection of the perpindicular and the circle. Then draw the segment to the other point so you have a triangle. Then where this segment and the circle cross draw the intersection. Then make the connection of this intersection to the point being connected to and draw a circle with that center. Where this circle crosses the orginal segment is the dividor.
To construct a pentagon given a side, first draw the segment. Then find the midpoint and draw the perpindicular. From here you can rotate the base segment by 108 degrees (360/5=72 and 180-72=108). From here you know have a point where the rotation and the circle meet. From this point you can then draw another circle to find the third point and successively the fourth and fifth.
21. Hexagon, given a side
To construct a hexagon, given a side, circles should be drawn from the two endpoints and then their intersection is the center of the hexagon. From here a circle can be drawn from the center that will intersect all of the points of the hexagon. Then two more point (D and C can be found). Finally to more points are found by doing circles from D and C. The intersections are marked adn connected and thus a hexagon is formed.
