Assignment 5

SCRIPT TOOLS

This file contains a list of script tools for GSP constructions.

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

2. The ORTHOCENTER (H) of a triangle is the point of intersection of the three altitudes.

3. The CIRCUMCENTER (O) of a triangle is the centre of the circle through the vertices and is therefore the point of intersection of the perpendicular bisectors of the three sides.

4. The INCENTER (I) of a triangle is the centre of the circle which is tangential to the three sides of the triangle. The Incentre is the intersection of the three interior angle bisectors.

5. The MEDIAL triangle is formed by joining the mid-points of the sides of the triangle.

6. The MID-SEGMENT triangle is the triangle formed by joining the midpoints from the orthocenter to each of the three vertices triangle.

7. The ORTHIC triangle is determined by the feet of the altitudes.

8. The PEDAL triangle of a point P, with respect to a triangle ABC lying in the same plane, is the triangle determined by the feet of the perpendiculars from P to the sides of triangle ABC. This script creates a pedal triangle for a point inside the triangle ABC.

9. For every triangle, there is a NINE-POINT circle which passes through the midpoints of the sides, the three feet of the altitudes, and the three EULER points. Note that the Euler points P₁, P₂ and P₃ are the midpoints of the segments joining the orthocenter H to the vertices. This script creates the nine-point circle for an acute-angled triangle.

10. This script TRISECTS a line segment.

11. Use this script to construct an EQUILATERAL triangle given a side.

12. Use this script to construct a SQUARE given a side.

13. Use this script to construct an ISOSCELES triangle, given

base and altitude.

14. This script generates the triangle CENTERS (Orthocenter

(H), Centroid (G), Circumcenter (O) and Incenter (I)).

Key

Centroid