Math 403, Spring 2007

Geometer’s Sketchpad Instructions for Fri. Feb. 2

1. In 239 Altgeld Hall, login using your netid and password or active directory password. Problems? Ask Dr. Mortensen or the lab attendant at the desk by the door.
   
   
2. Open the web browser Firefox and go to
   http://www.math.uiuc.edu/~kmortens/403-Sp07/gspfeb2.htm
   for these instructions.
   
   
3. Open Geometer’s Sketchpad (GSP). You can do this by clicking on the symbol (yellow circle with a triangle and a square in it) near the bottom of the page, or by finding Sketchpad under Applications.
   
   
4. Go to http://www.ettc.net/techfellow/sketch.htm for a two part tutorial in the basics of using GSP. You do not need to go through every detail of this. Depending on your personality and prior experience, you can either skim it now, trying out a few things, or you can go directly to the next step and just refer back to the tutorial when you need some information.
   
   
5. The first project is on the medians and centroid of a triangle. You can find it at
   http://www.teacherlink.org/content/math/activities/skpv4-centerstri2/home.html
   Click on “Activity Guide” and follow the instructions for Parts 1, 2, 3. You do not need to do Part 4. You won’t be turning anything in, and you don’t need to write any of the conjectures or proofs which are called for. However, think about the conjectures and be sure you do all the GSP constructions and measurements which are called for. You should observe that no matter how you drag the vertices of the triangle around, the three medians are always concurrent (share a common point). Be sure you understand how your work illustrates Theorem 1.4 from the textbook.
   
   
6. For your second project, you will use GSP to illustrate the Theorem of Ceva (Theorem 1.13 in the textbook).
   a. Use GSP to draw a triangle and label the vertices A, B, C.
   b. Construct a point on the side BC and label it A`. Note that you can drag A` around but it will always stay on BC. Similarly, construct B` on side AC and C` on side AB.
   c. Now measure the distances A`B, A`C, B`C, B`A, C`A, C`B and use the Calculate function (under the Measure menu) to calculate (A`B/A`C)(B`C/B`A)(C`A/C`B).
   d. Drag around the points A`, B`, C` and observe that the three lines AA`, BB` and CC` are concurrent exactly when (A`B/A`C)(B`C/B`A)(C`A/C`B)=1. (if you get a number within about .02 of 1, that is close enough.)
   e. Compare your work to the statement of Ceva’s Theorem in the textbook (Theorem 1.13 and the preceding paragraph). The author uses different notation and has -1 instead of 1. We’ll discuss all that later.
   
   
7. If you happen to have extra time, try using Geometer’s Sketchpad to illustrate Exercise 1.7, which says that the four midpoints of any quadrilateral form a parallelogram.