Dynamic geometry software like Geometer's Sketchpad allows you to construct and manipulate geometric figures. Such software can help you discover relationships among geometric figures, search for invariants (properties that do not change), and clarify the beginning stages of geometric proof. In this session, you will begin to use the tools of Geometer's Sketchpad to construct geometric figures and explore their properties.
If you are not familiar with The Geometer's Sketchpad software, or would like a refresher, go to the following tutorial.
This session assumes you can do the following with Geometer's Sketchpad: construct points and segments; construct points on objects; create midpoints; construct lines that are parallel or perpendicular to given lines; measure distances and angles; and perform calculations on your measurements. If not, or if you would like a refresher, please go to the tutorial.
Using Geometer's Sketchpad, look at the following ways that you can construct a circle:
Use the Circle Tool to draw a circle. Notice that wherever you ended your circle, another point appears. The distance of this point from the center defines the radius of the circle. What happens when you move that point? What happens when you move the center point?
Place two points anywhere on your sketch. Select them both, and construct a circle using the Construct menu. What happens if you select the points in the opposite order?
Place a point anywhere on your sketch, and then draw a segment in a different location. Select both objects, and use the Construct menu to construct another circle. What does the point do? What does the segment do? Try moving both around and changing the size of the segment.
Construct two circles that go through each other's centers. See if you can construct them so that there are only two points that are displayed, as in the graphic below:
Use the Circle Tool to construct a single circle. Then use the Circle Tool to construct a second circle, starting on your first circle and ending at its center. Make sure that you connect to the first circle's center, or you may end up with two circles that only look like they go through each other's centers. Close Tip
As you learned in Session 1, there is a difference between drawing a figure and constructing a figure. If you are using a pencil and manual drawing tools, constructing requires that you use a compass and a straightedge. When you construct an object using dynamic geometry software, you use the software's tools to give the figure the necessary characteristics.
The Geometer's Sketchpad ® 2001, Key Curriculum Press, Emeryville CA, 1-800-995-MATH