Geometer

Basic Geometer's Sketchpad Workshop

Geometer's Sketchpad is an incredible bit of software. It is very

dynamic software: GS can measure any length or distance

between two points, measure any angle, bisect any segment or angle,

find midpoints, construct circles, perpendicular bisectors, construct

parallel lines, find a locus of points, find the area of a region, graph

functions, plot points and a host of more complex geometric and

algebraic ideas. I have used Sketchpad for over eight years in the

classroom and found it to be a fantastic software package that brings

geometric ideas home to students. Sketchpad is primarily designed

for use with middle school, high school, and even college students.

The workshop is designed to give the teacher the basic skills

necessary to use GS and write basic lessons using GS as the tool.

Here's an example.

Theorem: A point on the perpendicular bisector of a segment is

equidistant from the endpoints of the segment.

How can you prove/illustrate this theorem? Geometer's

Sketchpad can easily prove/illustrate this theorem. Here's how!

First we'll start Sketchpad and using the segment/line/ray tool, draw

a segment of any length on the workspace. Then using the Construct

menu, construct the midpoint of the segment. Notice the dimensions,

Sketchpad can measure length or angles to the nearest thousandth.

Next, label the points of the segment (here's what it should look like

at this point.)

Now you need to construct the perpendicular bisector of the segment;

click on Construct and then Perpendicular Line. Now the sketch looks

like this.

Using the Point Tool, place two points anywhere on the Perpendicular

Bisector (I labeled these D and E ). Next, measure the distance from

A to D and B to D. (they are the same!) Do the same for A to E and

B to E . ( these are also the same measures). That should lead you to

a conclusion that any point that lies on the perpendicular bisector is

equidistant from the endpoints.