 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 1, Part C:
Folding Paper (40 minutes)

In This Part: Constructions | Constructing Triangles | Concurrencies in Triangles
More Constructions

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:  To construct the midpoint of a line segment, start by drawing a line segment on the patty paper.   Next, fold the paper so that the endpoints of the line segment overlap. This creates a crease in the paper.   The intersection of the crease and the original line segment is the midpoint of the line segment.  Problem C1 Draw a line segment. Then construct a line that is

 a. perpendicular to it b. parallel to it c. the perpendicular bisector of the segment (A perpendicular bisector is perpendicular to the segment and bisects it; that is, it goes through the midpoint of the segment, creating two equal segments.)  To construct a perpendicular line, consider that a straight line is a 180° angle. Can you cut that angle in half (since perpendicular lines form right angles, or 90° angles)? To construct a parallel line, you may need to construct another line before the parallel to help you.    Close Tip To construct a perpendicular line, consider that a straight line is a 180° angle. Can you cut that angle in half (since perpendicular lines form right angles, or 90° angles)? To construct a parallel line, you may need to construct another line before the parallel to help you. Problem C2 Draw an angle on your paper. Construct its bisector. (An angle bisector is a ray that cuts the angle exactly in half, making two equal angles.)   Session 1: Index | Notes | Solutions | Video