Have you ever seen an old, crooked barn that you were sure was about to collapse any day? What do you think causes buildings to be crooked? Would you know how to build a building that is not crooked?
Why It Matters
The first step of many construction projects is to “square the site.” This means making sure all corners are at 90 degree angles from the very beginning. If this doesn’t happen, all sorts of problems can occur later on because the stability of the overall structure will be weaker. If you had walls, doors, or cabinets to install later, they wouldn't fit correctly. If you had planned to put square tiles on the floor, they wouldn't fit the room. Before long, you'd have a real mess on your hands.
Imagine that you have to put four corner posts in the ground for a barn. You want the barn to have a rectangular base. What principles of geometry can you use to make sure that the base of the barn is a rectangle?
One answer lies in the properties of various kinds of quadrilaterals. What is unique about a rectangle as opposed to other parallelograms that are not rectangular? A rectangle has two pairs of opposite sides that must be equal in length. Is that enough to make it rectangular, though? This is where many people go wrong. All parallelograms have two pairs of equal sides. What more does a rectangular base need? It must have diagonals that are of equal length as well.
Can you think of a step-by-step process for squaring your site? In other words, can you think of a process for making sure that the base of your barn will be rectangular, after you establish the locations of the four corner posts?
See for yourself: http://www.youtube.com/watch?v=hxF7bABNbLE
Sam is building a rectangular barn. He puts the four corners in the approximate spots where he thinks they should be. He makes sure that the opposite sides are of the same length. Then he measures the diagonals from corner to corner. They are not the same length. He moves one of the corners of the barn in order to make the diagonals the same length. Sam’s barn is still not a rectangle! Why not? What has Sam done wrong? What should he have done differently to make sure that the base of his barn would be a rectangle?