Chapter 1
An Overview of Geometry
IN THIS CHAPTER
Surveying the geometric landscape: Shapes and proofs
Understanding points, lines, rays, segments, angles, and planes
Cutting segments and angles in two or three congruent pieces
Studying geometry is sort of a Dr. Jekyll-and-Mr. Hyde thing. You have the ordinary geometry of shapes (the Dr. Jekyll part) and the strange world of geometry proofs (the Mr. Hyde part).
Every day, you see various shapes all around you (triangles, rectangles, boxes, circles, balls, and so on), and you’re probably already familiar with some of their properties: area, perimeter, and volume, for example. In this book, you discover much more about these basic properties and then explore more advanced geometric ideas about shapes.
Geometry proofs are an entirely different sort of animal. They involve shapes, but instead of doing something straightforward like calculating the area of a shape, you have to come up with a mathematical argument that proves something about a shape. This process requires not only mathematical skills but verbal skills and logical deduction skills as well, and for this reason, proofs trip up many, many students. If you’re one of these ...
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