How many of our students begin the school year apprehensive and fearful of their geometry class? They enter the room having heard all sorts of horror stories about the dreaded two-column proof and all those theorems. Too often, geometry is taught mechanically with an emphasis on recalling facts. The NCTM's Curriculum and Evaluation Standards (1989) calls for a move away from geometry as a tour through a collection of predetermined Euclidean theorems and their proofs. Instead, they advocate greater attention to approaches using coordinates and transformations, to real-world applications and modeling, and to investigations leading to student-generated theorems and conjectures, with supporting arguments expressed orally or in paragraph form. As teachers, we search for activities that will involve our students in the study of geometry and help them to understand the “whys” behind the facts. The following activity employs several strategies to enable students to make conjectures, construct mathematical ideas, and use mathematics as a tool to communicate with others.
