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Geometers distinguish between a drawing and a construction. Drawings are intended to aid memory, thinking, or communication, and they needn't be much more than rough sketches to serve this purpose quite well. The essential element of a construction is that it is a kind of guaranteed recipe. It shows how a figure can be accurately drawn with a specified set of tools. A construction is a method, while a picture merely illustrates the method.
The most common tools for constructions in geometry are a straightedge (a ruler without any markings on it) and a compass (used for drawing circles). In the problems below, your tools will be a straightedge and patty paper. You can fold the patty paper to create creases. Since you can see through the paper, you can use the folds to create geometric objects. Though your "straightedge" might actually be a ruler, don't measure! Use it only to draw straight segments. Note 4
Throughout this part of the session, use just a pen or pencil, your straightedge, and patty paper to complete the constructions described in the problems. Here is a sample construction with patty paper to get you started:
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To construct the midpoint of a line segment, start by drawing a line segment on the patty paper. |
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Next, fold the paper so that the endpoints of the line segment overlap. This creates a crease in the paper. |
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The intersection of the crease and the original line segment is the midpoint of the line segment. |
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