1. VISUALIZING GEOMETRY WITH GSP; NURTURING CURIOUSITY AND UNDERSTANDING Armando M. Martinez-Cruz CSU Fullerton Amartinez-cruz@fullerton.edu Fernando Rodriguez Buena Park HS frodriguez@fjuhsd.k12.ca.us Presented at CMC South Palm Springs, CA Nov. 4, 2005 http://taselm.fullerton.edu

2. Outline of the Presentation AQITGSP A quick Intro to GSP (Transform menu and Scripts) Some Investigations Some Examples from Class Questions and Conclusions

3. Construct a triangle given three sides. Make a script for this construction.

4. Given triangle ABC, construct the three medians, m1, m2 and m3. Construct a triangle with sides m1, m2, and m3. Investigate the ratio of the areas

5. Given triangle ABC, construct the three angle bisectors, b[1], b[2] and b[3]. Construct a triangle with sides b[1], b[2] and b[3]. Investigate the ratio of the areas

6. In a right triangle, investigate the relationship between the areas shaded.

7. The sides of an irregular convex pentagon are extended to form a star. Find the sum of the measures of the vertex angles (marked) of the star.

8. Consider the prior investigation for an irregular hexagon, heptagon.

9. Questions and Conclusions