## The Geometer's Sketchpad Intro Lab Assessment, page 2

### Mike Riedy

Back to Assessment, Page 1

#### Part 3: Don't Get Lost - Ain't No Directions!

Now you will be making sketches without step-by-step guidance. You have already done all the things you will be asked to do, and the GSP Introductory Lab can be used as reference.

Below you will find two equations of a line. Start with a new sketch. Find two points on each line, plot the points, draw the line, and measure the equation. List the two points you use below each equation.

```    a.  y = 2x + 1      b.   y = - 3x - 4

__X_|_Y__             __X_|_Y__
|                     |
|                     |
|                     |

```
Once the lines have been graphed and the equations are visible on the screen, put your name on the screen and print the sketch according to the same method you used at the end of part 2.

This section is all based on the Cusp and Saucers lab. If you didn't do that activity, you may skip this section.

Make a Spirograph Machine. Don't worry about remembering which point is Roger, which points are Bert and son, and which points are Ernie and son - just make the Spirograph Machine. Without adjusting any radii, run the machine and print the results. Make sure your name is on the screen and that the trace prints.

1. Adjust the radii to create a trace that is in phase with six cusps.

Explain how you created this trace (not how you created The Spirograph Machine):

___________________________________________________

___________________________________________________

Make sure the radii measurements and your name are on the screen before you run The Machine. Print the trace.

2. Have The Machine trace a perfect circle.

Explain how you created the circle trace:

___________________________________________________

___________________________________________________

Make sure the radii measurements and your name are on the screen before you run the Spirograph Machine. Print the trace.

3. Extra Credit: If time allows, create a Spirograph Machine with a circle on a circle on a circle. Set the radii so that the Machine creates a trace that is in phase and has a pattern. Print the trace as described in number 2.

Start with a new sketch. Draw a circle, construct a radius of the circle, and a place a point outside the circle.

1. Have the computer construct a line parallel to the radius through the point outside the circle.
2. Have the computer construct the line perpendicular to the first line through the center of the circle.
3. Place a point at the intersection of the two lines.
4. Construct the angle bisector of any one of the angles on the screen.
Put your name on the screen and print the sketch according to the same method you used at the end of part 2.

Draw or construct an equilateral triangle. Prove that it is equilateral by measuring all three sides.

What are the measurements of the three angles?  ______________ ______________ ______________ <1 <2 <3

Make sure your measurements are visible on the screen, put your name on the screen, and print the sketch in the same way you did at the end of part 2.