This is a geometry based lesson for a Pre-Algebra class. It is assumed that students have already learned what parallel and perpendicular are and understand what parallel and perpendicular lines are. This unit uses Geometer's Sketchpad to help students construct their own knowledge about polygons, particularly triangles and quadrilaterals. The lessons are planned for 45-50 minute periods.

**Objectives:** Students
will be introduced to and explore with Geometer's Sketchpad.

**Materials:** GSP
on student computers and worksheet shown below

Day 1 will start with a short review of parallel
and perpendicular. I will then introduce GSP to my students. Students
will not be on the computer yet. I will do a demonstration of
the different functions and buttons in GSP. Students will be asked
to take notes on what is shown to them about GSP in order to help
them out when they begin exploring and familiarizing themselves
with GSP. After a short discussion and introduction, students
will being on the following exercise taken from *Exploring Geometry
with Geometer's Sketchpad* published by Key Curriculum Press.

NAME:________________________

In this activity, you'll experiment with drawing, dragging, measuring, and labeling points, segments, rays, and lines. These objects, along with circles, are the building blocks of most geometric constructions.

**Sketch and Investigate: Points and Segments**

Note: If at any time you think you've made
a mistake or you want to do something differently, you can always
undo as many steps as you like. The **Undo** and **Redo**
commands are in the **Edit** menu.

1. The Point tool:

Highlight the

Pointtool and click in the sketch to construct a point. Click again to construct a second point. Notice that the most recently constructed point isselected: It appears with a bold outline.

2. The Selection Arrow:

Highlight the

Selection Arrowtool and click in a blank area in the sketch. This deselects everything.

3. The Text tool:

Highlight the

Texttool. Position the finger over a point and click to display that point's label. Display the other point's label, too.

4. With the **Selection Arrow** tool, click
on one point, press and hold down the **Shift** key on your
keyboard, then click on the other point. Now both points should
be selected (they should both be outlined).

5. In the **Measure** menu, choose **Distance**.
This will give you a line of text that says something like AB
= 1.4 inches.

6. Click in the blank area of your sketch to deselect the points, then drag one of the points. Observe the measurement.

How can you make the distance between the two points zero?

Answer:______________________________________________________________

7. The **Segment** tool:

Highlight the

Segmenttool and draw a segment connecting the two points. Two little black square on the segment indicate that it is selected.

8. While the segment is selected, go to the
**Measure **menu and choose **Length**. Again, a text will
show up that tells you the length of the segment.

9. Use the **Selection Arrow** tool to drag
either endpoint of the segment.

How does the length of a segment compare to the distance between its endpoints?

Answer:_____________________________________________________________

10. In the **File** menu, choose **New
Sketch**.

11. Press and hold down the mouse button on
the **Segment** tool. A palette of straight object tools will
pop out to the right. Drag right and choose the **Ray **tool.

12. Draw a ray in your sketch. Notice that the ray extends in one direction beyond the edge of your sketch window.

13. Use the **Text** tool to show the labels
of the ray's control points.

14. Use the **Selection Arrow** tool to
drag each point to observe how it controls the ray.

A ray with endpoint A that passes through a point B is called ray AB. Could it just as well be called ray BA? Explain why.

Answer:____________________________________________________________

___________________________________________________________________

15. Select the ray and press the **Measure**
menu. Note that **Length** is grayed out.

Why do you think you can't measure the length of a ray?

Answer:_____________________________________________________________

16. With the ray still selected, press the
**Construct **menu and look at your choices. Choose **Point
on Object**.

Why can't you construct the midpoint of a ray?

Answer:_____________________________________________________________

17. Drag the new point to see how its behavior compares to that of the ray's two control points.

Give two different names for the ray shown under #16. Use only two points in each name.

Answer:_____________________________________________________________

18. Press and hold down on the **Ray **tool,
then drag right to choose the **Line** tool.

19. Experiment by drawing lines in your sketch.

List all the similarities and differences you can between segments, rays, and lines.

Answer:_____________________________________________________________

____________________________________________________________________

____________________________________________________________________

20. Name two rays and a segment that lie on the line below.

Answer:_____________________________________________________________