An Introduction to Geometer s Sketchpad

An Introduction to Geometer’s Sketchpad Kimberly M. Childs, Ph.D. Deborah A. Pace, Ph.D. Thomas W. Judson, Ph.D. Stephen F. Austin State University ...
Author: Lambert Norman
0 downloads 0 Views 110KB Size
An Introduction to Geometer’s Sketchpad

Kimberly M. Childs, Ph.D. Deborah A. Pace, Ph.D. Thomas W. Judson, Ph.D.

Stephen F. Austin State University Department of Mathematics and Statistics

Introduction Geometer’s Sketchpad (GSP) is a computer program that allows you to do straightedge and compass constructions on the computer. To access GSP, double-click on the GSP icon. On the top of the window, you will see the various menu options. • • • • • • • •

File, for opening, closing, saving, and printing documents. Edit, for selecting objects, editing object properties, and setting preferences. Display, for changing the appearance of drawings. Construct, for constructing figures. Transform, for translating, rotating, dilating, and reflecting objects. Measure, for displaying measurements and making calculations. Graph, for options with coordinate axis and function plots. Help.

On the left-TEXT side of the window, you will see icons for various GSP tools. • • • • • •

Selection Arrow. Click on objects to select them. Point Tool. Click to create a point on the window or an object. Compass (Circle) Tool. Click to create a center click on the window, then click elsewhere to create a radius point. Straightedge (Segment) Tool. Click to create one endpoint, then click to create the line segment. Text Tool. Drag in a blank area to create a caption. Click on an object to display or hide a label. Custom Tool. Create your own tools.

For more information, see Appendix III in your textbook.

Investigation 1: Quadrilateral Midpoints Dr. Deborah Pace (Note: To perform most of the instructions below, you need only use the left mouse button, holding it down to “drag”. Remember to hold down the SHIFT key to select more than one object at a time.) 1.

Use the segment drawing tool on the left of your screen to make a quadrilateral.

2. With the ARROW button highlighted, SELECT all four segments in order. (Remember to hold down the SHIFT key to select more than one object at a time.) 3. With the ARROW button, choose [CONSTRUCT] [POINT AT MIDPOINT] from the menu bar at the top of the screen. 4. With all four midpoints still selected, use the ARROW button to choose [CONSTRUCT] [SEGMENT] from the menu bar at the top of the screen. 5.

With your mouse, “click” anywhere on the screen to DESELECT all selected objects.

6. With the TEXT button on the left side of your screen highlighted, click on each midpoint to label. 7. With the ARROW button highlighted, point to one of the vertices of the quadrilateral and “drag” that vertex, noting what happens to the shape of the figure connecting the midpoints as you distort the shape of the original quadrilateral. 8. Note the shape created by the connected midpoints. What do you think the shape is? Make a conjecture.

The shape formed by connecting the midpoints of all four sides of any quadrilateral is a __________________________.

Investigation 2: Angles Inscribed in a Semicircle Dr. Deborah Pace 1.Use the circle drawing tool to make a circle. 2.Click anywhere on the screen to deselect all. 3.With the straightedge tool on “line”, SELECT the point on the circle and the center of the circle. (Remember to hold down the SHIFT key to select more than one object at a time.) Choose [CONSTRUCT][LINE]. 4.With the ARROW key, SELECT the circle and the line. 5.Choose [CONSTRUCT][POINT AT INTERSECTION]. 6.Choose [CONSTRUCT][SEGMENT]. 7.SELECT the line. (Make sure nothing else is selected.) Choose [DISPLAY][HIDE LINE]. 8.SELECT the circle. Choose [CONSTRUCT][POINT ON OBJECT]. 9.SELECT the point on the circle and the two endpoints of the diameter. Choose [CONSTRUCT][SEGMENT]. 10.

With the TEXT tool selected, click on the three vertices of the constructed triangle to label.

11. With the ARROW key, SELECT the three vertices of the triangle, making sure the point on the circle is the interior vertex. 12.

Choose [MEASURE][ANGLE]. Click anywhere on the screen to deselect all.

13.

Measure the other two angles of the triangle.

14. With the ARROW key selected, hold down the left mouse button and “drag” the point on the circle. Observe the measure of the angle. 15.

Make a conjecture.

The measure of any angle inscribed in a semicircle is _________.

Investigation 3: Pythagorean Theorem Dr. Deborah Pace 1.With the SEGMENT tool, draw a segment. (Holding down the SHIFT key will create a horizontal segment.) 2.With the ARROW key selected, SELECT the segment and one endpoint. (Remember to hold down the SHIFT key to select more than one object at a time.) 3.Choose [CONSTRUCT][PERPENDICULAR LINE]. 4.Choose [CONSTRUCT][POINT ON OBJECT]. 5.SELECT the two points shown on the line and choose [CONSTRUCT][SEGMENT]. 6.SELECT the line. (Be sure it’s the line and NOT the segment!) Choose [DISPLAY][HIDE LINE]. 7.SELECT the endpoints not connected and choose [CONSTRUCT][SEGMENT]. “Drag” the vertices of the triangle and notice it remains “right” because of the way you constructed it! 8. Construct squares on each side of the right triangle, comparing their areas. 8a) 8b) 8c) 8d) 8e)

SELECT one vertex. Choose [TRANSFORM][MARK CENTER]. SELECT the new segment and other endpoint of the segment. Choose [TRANSFORM][ROTATE][90 degrees]. SELECT the endpoint of the new segment and choose [TRANSFORM][MARK CENTER]. 8f) SELECT the new segment and other endpoint of the segment and choose [TRANSFORM][ROTATE][90 degrees]. 8g) SELECT the endpoints and choose [CONSTRUCT][SEGMENT]. 8h) SELECT all four vertices on the constructed square. Choose [CONSTRUCT][POLYGON INTERIOR]. Choose [DISPLAY][COLOR] and select color. 8i) Repeat steps 8a) through 8h) on the other two segments of the triangle. 8j) With the TEXT tool, label all points. 8k) SELECT all three polygon interiors. Choose [MEASURE][AREA]. 8j) SELECT the areas of the two smaller squares and choose [MEASURE][CALCULATE] to add the areas. (Selected measures are under VALUES.)

Suggest Documents