Assignment 5

Geometer Sketchpad
Scripts


 
1. Centroid

The centroid (G) of a triangle the common intersection of the three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side.

 

Click on the picture to explore the location of the centroid for various triangles.


Click Here
to see the script for the construction of the centroid of a triangle.

2. Orthocenter

The orthocenter (H) of a triangle is the common intersection of the three lines containing the altitudes. The altitude is a perpendicular segment from a vertex to the line of the opposite side.

Click on the picture to explore the location of the orthocenter for various triangles.


 

Click Here to see the script of the construction of the orthocenter of a triangle.


3. Circumcenter

The circumcenter (C) of a triangle is the point in the plane equidistant from the three vertices of a triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by two points, C is on the perpendicular bisector of each side of the triangle.

Click on the picture to explore various locations of the circumcenter for various triangles.


 

Click Here to see a script for the construction of the circumcenter of a triangle.



4. Circumcircle

The circumcircle is created with the circumcenter (C) as its center. The vertices of the triangle are located on the circumcenter.

Click the picture to explore the circumcircle for various triangles.


 

Click Here to see a script of the construction of the circumcenter of a triangle.


5. Incenter

The incenter (I) of a triangle is the point on the interior of a triangle that is equidistant from the three sides. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle.

Click the picture to explore the location of the incenter for various triangles.


 

Click Here to see a script for the construction of the incircle of a triangle.


6. Incircle

The incircle of a triangle is constructed with the incenter (I) as the center. The radius of the incircle is a perpendicular segment from the incenter to a side. The incircle is tangent to the sides of the triangle.

 

Click the picture to explore the incircle of various triangles.



Click Here to see a script for the construction of the incircle of a triangle.


7. Medial triangle

The medial triangle is created by connecting the midpoints of a triangle.


Click the picture to explore the properties of the medial triangle for various [original] triangles.


Click Here to see a script for the construction of a medial triangle.


7a. Orthocenter, Mid-segment triangle.

The orthocenter, mid-segment triangle is created by connecting the midpoints of the segments HA, HB, and HC.

Click the picture to explore the properties of this triangle.


Click Here to see a script for the construction of a triangle created by the midsegments of the orthocenter and the original triangle. 



8. Orthic triangle

The orthic triangle is constructed by connecting the feet of the altitudes of a triangle.

Click the picture to explore the properties of the orthic triangle.


 

Click Here to see a script of the construction of the orthic triangle.


9. Pedal triangle

The pedal triangle is created by selecting an arbitrary point (p) that can be either inside or outside the triangle. The triangle is created by creating a perpendicular line from the lines that create the original triangle to the pedal point. The intersection of these lines is then used to form the pedal triangle.


Click the picture to explore the pedal triangle for various [original] triangles.



Click Here to see the script for the construction of the pedal triangle for any triangle.



 
10. Center of Nine point circle

The nine point circle is created by the midpoints of AB, BC, and AC; the points at the feet of the altitudes; and the midpoints of the segments connecting the vertices of triangle ABC to the orthocenter.

Click the picture to explore the points on the nine point circle for various triangles.




Click here to see a script for the construction of a nine-point circle.

 

11. Nine Point Circle

The nine point circle is created by the midpoints of AB, BC, and AC; the points at the feet of the altitudes; and the midpoints of the segments connecting the vertices of triangle ABC to the orthocenter.

Click the picture to explore the points on the nine point circle for various triangles.

Click here to see a script for the construction of a nine-point circle.


 
12. Trisecting a line segment



Click Here to see a script for the trisection of a line segment.



13. Equilateral triangle, given a side

An equilateral triangle is a triangle whose sides are equal. The triangle ABC was constructed using the given side AB.

 

Click the picture to manipulate the equilateral triangle for any length AB.

Click Here to see the script for the construction of an equilateral triangle given the side AB.

 
14. Square, given a side

Click the picture to manipulate the square for any length of segment AB.


 Click Here to see a script for the construction of a square given a side.

15. Isosceles triangle, given base and altitude

An isosceles triangle is defined as a triangle that has two equal sides and two equal bases.

Click the picture to manipulate the length of the base (MN) and the altitude (QP) and the shape of the isoceles triangle.


Click Here to see a script for the construction of an isosceles triangle given a base and an altitude. 


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

Click the picture to explore the locations of the centers of ABC for various triangles.

Click Here to see a script for the construction of the centers of a triangle.

17. Triangle Centers (H, G, C, and I) with the Euler Line

Click the picture to explore the location of the centers of ABC and the Euler Line for various triangles.


Click Here to see a script for the construction of centers of the triangle ABC.
 


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

Click the picture to find the locus of the vertex of a fixed angle that subtends a fixed segment (or look below to find out what the locus looks like).


Click Here to see a script for the construction of a fixed angle that subtends a fixed segment.

Below is a picture of the locus.



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

Click the picture to investigate line AB that has been divided into the golden ratio.

Click Here to see a script that allows you to divide any segment into the golden ratio.

 
20. Pentagon, given a diagonal.

Click the picture to manipulate the length of AB and the size of the pentagon.


Click Here to see a script for the construction of a pentagon given a diagonal. 

21. Pentagon, given a radius.

Click the picture to manipulate the radius and the pentagon.


Click here to see a script for the construction of a pentagon given a radius.


22. Pentagon, given a side.

Click the picture to manipulate line segment Q'R' and the size of the pentagon.

Click here to see a script for the construction of a pentagon given a side.
 

23. Hexagon, given a side.

Click the picture to manipulate the length of AB and the size of the hexagon.


Click Here to see a script for the construction a hexagon with a given side AB. 

24. Octagon, given a side.

Click the picture to investigate the octagon given different lengths of AB.

 

Click Here to see a script for the construction of an octagon given a side.


25. Octagon, given a radius

Click the picture to investigate the octagon given different lengths of CD.

Click Here to see a script for the construction of an octagon given a radius.


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