Getting to Know Geometer’s Sketchpad - Triangles & Spinwheels

Welcome too the Geometer’s Sketchpad, an exciting and useful tool for students of all ages. With Sketchpad,
you can explore geometry in ways you never would be able to do otherwise. In this section, you will learn
Sketchpad skills that you will use in doing activities and projects. Feel free to explore on your own.

Open Sketchpad. You should see this:



This is your “sketch pad.”

On the left side of the sketch you will see the toolbox. Each tool has a specific purpose
that is summarized below.



You will learn how to use each of them in this first activity.

Draw some points on your sketchpad.

Click on the point tool. You will notice that your pointer arrowhead has a point at the end of it.
Move to a spot where you want a point and click. Repeat so you have 5 points.

Move the points around.
In order to move the points around you have to first click on the selection arrow tool .
Notice that the point you select is highlighted. Now move it around.
Repeat for another point. Can you move more than one point at a time?

Deselect your points by clicking in any white space on the pad.
Now select more than one point and drag them.

Undo your work (in other words, use the  Oops keys.)

Look at your menu bar. There you will see Edit. Click and select undo. Repeat.
Notice that you are undoing every step you took.
Continue until you have only 3 points.

Note on undoing: You can use the keystrokes CTRL Z to accomplish the same thing. CTRL and Z when used together are called the Oops keys. Do you know why?)

Draw a line segment.

Click on the segment tool. Draw a segment. Move the segment around. (Hint: Click on the selection arrow tool to move your segment.
Deselect. Choose one of the end points and spin it around. Repeat for the other endpoint. Notice that you can also change the length of the line when you are doing this.

Draw a Triangle using the line segment tools.



Move each of the corners (better known as vertices) of the triangle around.

Click on the selection arrow, select a corner and spin.
Repeat for the other vertices. (This is called Sketchpad aerobics.)

Add Color to the triangle.

Deselect (Click in a white area.)
Click on and highlight all of the vertices so all three are highlighted.
 
Make a triangle interior.

Go to the Construct menu and choose Triangle Interior.
At this time your triangle should be highlighted.

deselected

selected

Make a spinwheel of triangles.

Select one the points of the triangle. This point will be the point of rotation.
Double click on the point. You should see the point expand and then shrink.
Go to the transform menu and choose rotate. 
Enter 60 degrees.
Click OK.
Go back and choose rotate again. Continue until you have “completed” the pinwheel.
Change the colors of each triangle by right clicking the mouse and choose color.

Test your pinwheel.

Grab any vertex on the original triangle and drag it around.
You should notice that all the shapes change. Why do you think that is happening?

Part 2. Animate the pinwheel.

Draw a circle anywhere on your sketch.

Deselect.
Select a vertex on your original triangle.
Select the circle. (You will have a point and the circle highlighted.)
 

Go to the Edit menu and choose Merge Point to Circle. The vertex should move and attach to the circle.

Make an animation button.

Go to the Edit menu and choose the action button followed by animation. You should see this prompt:

Click on OK and you will see an animate button appear.
 
Do the animation.

Click on the button and your animation should begin. Click on the button to stop.
Move the circle to another place. Make it smaller. Click on Animate point again.

Once you have one you like, hide the circle. (highlight the circle and press CTRL H)

Some Questions.

1. Repeat this activity with other angles of rotation like 90, 120, 45, and 30.

2. How many triangles does it take to complete the pinwheel if the angle is 90? Why?

3. How many triangles does it take to complete the pinwheel if the angle is 120? Why?

4. How many triangles does it take to complete the pinwheel if the angle is 30? Why?

5. How many triangles does it take to complete the pinwheel if the angle is 45? Why?

6. Print out your favorite pinwheel!