One objective in #1 & 2 below is to create a script that takes any two given points and, when played, constructs an unmess-upable square having the segment joining those two given points as an edge of the square. Thus, by playing the script, you'll always have an electronic version of a square sheet of origami paper.

Constructing a Square (that remains a square):

1. To construct a square that is unmess-upable, start by listing properties it has. Think about how it is distinguished from other quadrilaterals, how it is distinguished from other parallelograms, how it is distinguished from other rectangles, how it is distinguished from other rhombuses. State properties below to assure that you have a square:

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2. Open a new sketch, draw two points anywhere in the sketch plane, and then construct a square so that if you drag any of the four vertices or drag any of the four sides, the square will move, but it will remain a square. (Thus, someone could mess up the size and orientation of your square just by dragging one of the given points, but the shape would remain invariant. If a side is dragged with the translate tool (also called the Select tool, only the position of the square should change.) Be sure to actually test your result!

Once you have made sure your sketch is unmess-upable, make a script for the process, showing the script view so that you can see the verbal description of Given and Steps for the process. As one test for your script, only the two "random" points should be listed as Given. Once you are sure your script has the desired properties, save the sketch (file) in your web space, and print the script to document the process you used. (See Lab 3 for making a script. To print the script, hold down the control button and click on any object in the script view. (Just right-click in the Windows version.) Then select Print Script View from the pop-up menu.) The example script pictured below illustrates one method for constructing a square. Be sure that your script uses a different method, but starts with just two given points.

Using Sketchpad to construct the creases resulting from the process of folding an equilateral triangle from a square:

3. Now that you have a square, it would be nice to make a sketch to construct the creases (line segments) made during the process of folding an equilateral triangle from a square.

For this lab, you need construct only the midline, the critical point on the midline, and the first crease made following the midline crease. You needn't go beyond that for the lab, since there are many different approaches to finishing the construction. Finishing it off in your own way is Problem 12.

Lab details:

a. Start with a Sketchpad square with a square of paper at the side. Then construct (in a Sketchpad unmess-upable way) the midline crease.

b. Now determine, thinking about how you fold onto the midline, how Sketchpad could do it. Use a Sketchpad construction to locate, in a Sketchpad unmess-upable way, the point on the midline.

c. Finally, construct the second segment on the square, the one corresponding to the second crease on the paper. This will involve constructing some additional objects with Sketchpad.

d. Save your file when you're done, and print the resulting sketch or sketches.