Consider various GSP tools.

                                 By Na Young

 

1.  Centroid

 

2.  Orthocenter

 

3.  Circumcenter

 

4.  Circumcircle

 

5.  Incenter

 

6.  Incircle

 

7.  Medial triangle

 

8.  Orthocenter, Mid-segment triangle.

 

9.  Orthic triangle

 

:Given a triangle , the triangle  whose vertices are endpoints of the

 altitudes from each of the vertices of  is called the orthic triangle,

or sometimes the altitude triangle.

 

10. Pedal triangle

: Given a point P, the pedal triangle of P is the triangle whose polygon

 vertices are the feet of the perpendiculars from P to the side lines.

 

10.     Center of Nine point circle

 : It is the midpoint of the line between the circumcenter and orthocenter.

 

12.      Nine Point Circle

: The nine-point circle, also called Euler's circle or the Feuerbach

circle, is the circle that passes through the feet of the perpendicular,

 and  dropped from the vertices of any triangle  on the sides opposite

them.

 

13.     Trisecting a line segment: We use the Centroid divide

      a segment from a vertex to an opposite side a ratio 2:1

 

14. Equilateral triangle, given a side

 

15. Square, given a side

 

16. Isosceles triangle, given base and altitude

 

17. Triangle Centers (H, G, C, and I)

 

18. Triangle Centers with Euler Line

 

 

19. Locus of vertex of a fixed angle that subtends a fixed segment.

       Circle.

 

20. Divide a segment AB into two parts that form a golden ratio..

 

21. Pentagon, given a radius.

     Make a circle by given a radius and in a coordinate system,

      Rotate 108 degrees.

 

22. Pentagon, given a side.

        Using Rotate by 108

 

23. Hexagon, given a side.

       Using Rotate by 60

 

24. Octagon, given a side

        Using Rotate by 36