Math 487 Lab 1

Location

Math Sciences Computer Lab, CMU B027 (Communications Building)

How to get Started

Log into the PC using user name Lab and leaving the password field blank. The Sketchpad icon is the one with the triangle and circle in the Math Applications folder. Start the GSP (Geometer’s Sketchpad) program

Materials needed

  1. GASP4: Getting Acquainted with Geometer’s Sketchpad 4, Chapter 1, Sections 1.1 — 1.4. (This link goes to a pdf file that can be read online during lab. It can be printed if you prefer a paper copy.)
  2. GTC: Geometry Through the Circle, Sections 3.2 and the first part of 3.3. (This link goes to a pdf file that can be read online during lab. It can be printed if you prefer a paper copy.)
  3. File storage: You will want to save some of your work from the lab. While one option is to bring a diskette to the lab, a better option is to use file transfer to move the files to your "u" student account on Dante. Note the files can be used on Mac or Windows. Just be sure that the file name ends in .gsp.

Results: What to produce and turn in by the end of lab

Work in groups of 3 or 4. There should be one paper per group. Be sure everyone is on board with all the answers.

  1. Write answers to the questions in GTC 3.2 and 3.3.
  2. Study the properties of isosceles triangles and how than can be proved with the congruence tests SAS, ASA, SSS. Write down what you can show and how you show it.

Note: The answer to the second question should go a long way to providing a solution to Assignment 1.

Lab Plan

1. Introduction to Geometer's Sketchpad tools using GASP

Work through the four Sections 1.1 -- 1.3 of GASP.

2. Constructions using menus -- perpendicular bisectors, etc.

Work through Section 1.4 of GASP, but do it briskly.

3. Exploring equal distances, circles of equal radius and the perpendicular bisector.

Work through GTC Section 3.2 (saving the Explore More for later) and Investigation 1 of 3.3. Think about the relationship between perpendicular bisectors and distance. As a group, write answers to the questions.

4. Constructing triangles from data such as SAS, ASA, SSS.

Follow this link for exploration of triangle congruence.

Create at least some of these figures, especially the SSS figure.

5. Isosceles Triangles

This link goes to some constructions for isosceles triangles. There are 4 tasks on this page. In your group divide up the tasks. You will see that the results are very similar. But the congruence criterion that you can use to prove the result may be different. Write down your conclusions to be turned in.

Extra: Construction problem: construct a square.

Draw a segment AB in a blank figure. Then construct points C and D so that ABCD is a square (and remains a square when one drags A or B). If you succeed one way, can you find one or more other ways to carry out the same construction?