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Michelle E. Chung
* EMAT6680 Assignment 5: Michelle's GSP Script Tools


* Please click the title if you want to see the script. (Attention: You need Sketch Pad to see them.)

 

1. Centroid The CENTROID(G) of a triangle is the common intersection of the three medians.

2. Orthocenter

The ORTHOCENTER(H) of a triangle is the common intersection of the three lines containig the altitudes.

3. Circumcenter

The CIRCUMCENTER(C) of a triangle is the point in the plane equidistant from the three vertices of the triangle.

4. Circumcircle

The CIRCUMCIRCLE of a triangle is a circumscribed circle that passes three vertices of the triangle, and its center is the circumcenter.

5. Incenter

The INCENTER(I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides.

6. Incircle

The INCIRCLE of a triangle is a inscribed circle whose center is the incenter.

7. Medial triangle

The MEDIAL TRIANGLE is a triangle with vertices as the midpoints of the triangle.

8. Orthocenter, Mid-segment triangle

The MID-SEGMENT TRIANGLE is a triangle that is formed by mid-segments of a triangle, which are the line segments joining midpoints of two sides of a triangle.

9. Orthic triangle

The ORTHIC TRIANGLE is a triangle joining the feet of the altitudes of the triangle.

10. Pedal triangle

The PEDAL TRIANGLE is a triangle whose vertices are the feet of perpendiculars from each vertex of the triangle to their opposite sides in the triangle.

11. Center of Nine point circle

The CENTER OF NINE POINT CIRCLE is the center of the nine point circle.

12. Nine Point Circle

 

The NINE POINT CIRCLE is a circle that passes through nine significant points, six lying on the triangle itself (unless the triangle is obtuse). They include:

  • The midpoint of each side of the triangle
  • The foot of each altitude
  • The midpoint of the segment of each altitude from its vertex to the orthocenter (where the three altitudes meet)

13. Trisecting a line segment

This is how to draw TRISECTING points of a LINE SEGMENT.

14. Equilateral triangle, given a side

The EQUILATERAL TRIANGLE is a triangle that has three congruent sides.

  • This is how to draw a EQUILATERAL TRIANGLE with GIVEN SIDE.

15. Square, given a side

The SQUARE is a quadrilateral that has four congruent sides and four congruent angles.

  • This is how to draw a SQUARE with GIVEN SIDE.

16. Isosceles triangle, given base and altitude

The ISOSCELES TRIANGLE is a triangle that has two congruent sides.

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

The FOUR CENTERS OF TRIANGLES are ORTHOCENTER(H), CENTROID(G), CIRCUMCENTER(C), and INCENTER(I).

18. Triangle Centers with Euler Line

The EULER LINE of a triangle is a line that passes the Center of nine point circle, the Circumcenter(C), Centroid(G), and Orthocenter(H) of the triangle.

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

This is how to draw a LOCUS of the VERTEX of a FIXED ANGLE that SUBSTANDS a FIXED SEGMENT.

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

The GOLDEN RATIO, phi, is 0.6180339887...

  • A GOLDEN RATIO of a LINE SEGMENT is the ratio that is the length of the larger portion of the line segment to the length of the whole line segment.

21. Pentagon, given a radius

The PENTAGON is a polygon that has five sides.

  • This is how to draw a PENTAGON with GIVEN RADIUS.

22. Pentagon, given a side

The PENTAGON is a polygon that has five sides.

  • This is how to draw a PENTAGON with GIVEN SIDE.

23. Hexagon, given a side

The HEXAGON is a polygon that has six sides.

  • This is how to draw a HEXAGON with GIVEN SIDE.

24. Octagon, given a side

The OCTAGON is a polygon that has eight sides.

  • This is how to draw a OCTAGON with GIVEN SIDE.

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