Janet Kaplan __________________________________________________________________________________________________

 

The following is a library of scripts from Geometer's Sketchpad that can be used as templates for further work in GSP.

 

1) CentroidIntersection of the medians of a triangle. Medians are segments drawn from a vertex to the midpoint of the opposite side.

2) Orthocenter Intersection of the altitudes of a triangle. Can be inside or outside of triangle.

3) Circumcenter Intersection of three perpendicular bisectors of the sides of a triangle. It is the center of a circumscribed circle.

4) Circumcircle This circle is constructed with the circumcenter as the center and the vertices of a triangle as points on the circle. It is also known as the circle around an inscribed triangle.

 

5) Incenter Intersection of three angle bisectors of a triangle. It is the center of the inscribed circle and is equidistant from all three sides of the triangle. ††

 

 

6.) IncircleAlso known as the inscribed circle, it is tangent to the sides of the triangle, with its center at the incenter.

7) Medial triangle A triangle formed by connecting the midpoints of the sides of a triangle. The length of the segments is one-half that of the original triangle.

8) Orthocenter of Mid-Segment Triangle Orthocenter of medial triangle

9) Orthic TriangleTriangle formed by connecting the segments of the feet of the altitudes.

10) Pedal Triangle†† The Pedal Triangle of any triangle is generated by taking a point P anywhere on the plane, and constructing perpendicular lines from P to each side of the triangle. The points of intersection of these lines with the sides of the triangle become the vertices of the Pedal Triangle.

11) Nine Point CenterCenter of the Nine Point Circle (U). This point is collinear with the Euler Line.

There are several ways of pinpointing the center from the Nine-Point Circle. One way is to use the intersection of the diagonals of rectangle LMYZ.

12) Nine Point Circle Circle that includes the three midpoints of the sides of a triangle, the three feet of the altitudes, and the three midpoints of the segments from the vertices to the orthocenter of the triangle. (see diagram above)

13) Trisecting a Line SegmentIt's not as straight forward as you might think!


14) Equilateral triangle, given a side.

15) Square, given a side.

16) Isosceles Triangle, given base and altitude.

17)Triangle CentersThe Centers of a triangle include the Orthocenter, the Circumcenter, the Centroid and the Incenter.

18) Euler Line This line contains the orthocenter, circumcenter and centroid of the triangle.

 

 

19) The Golden Ratio Isn't it beautiful?

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