This lab is adapted from an exercise on pages 1-2 in Henderson, David W., "Straightness and Symmetry", Experiencing Geometry on Plane and Sphere, Saddle River, New Jersey: Prentice Hall, 1996.

Think back to your experiences with lines - in this course, perhaps, but also prior to the course. It might help to think about how you would explain straightness to a 5-year-old (or how the 5-year-old might explain it to you!). If you use a "ruler," how do you know if the ruler is straight? How can you check it? What properties do straight lines have that distinguish them from non-straight lines?

We'll look at the question in four related ways:

1. How do you construct something straight, say, lay out fence posts in a straight line, or draw a straight line?

2. How can you check in a practical way if something is straight without assuming that you have a ruler, for then we will ask, "How can you check that the ruler is straight?"

3. What symmetries does a straight line have? A symmetry of a geometric figure is a reflection, rotation, translation, or composition of them which preserves the figure. For example, the letter "T" has reflection symmetry about a vertical line through its middle, and the letter "Z" has a rotation symmetry if you rotate it half a revolution about its center.

4. Finally, based on your work in the three questions above, write a definition of "straight line"?