Thousands of years ago, the Egyptians developed techniques to measure the amount of land a person owned. They used this information to collect taxes. Later, the Greeks formalized this process of measurement into a branch of mathematics we call geometry. The word geometry comes from the Greek words for “Earth measurement.” Today, geometry is used in many different ways. We use geometry when we do home improvement projects, buy carpeting, or work in the garden. And it is used by people in different careers like interior design, air traffi c control, science, construction, and many more. In this chapter, we will learn some basics of geometry beginning with some terms. 1 Identify Lines, Line Segments, and Rays Space is an unlimited, three-dimensional expanse. The Earth is an example of an object in space. A plane is a fl at surface that continues indefi nitely. A fl oor is part of a plane, as is a wall or a piece of paper. The most basic concept in geometry is a point. A point is a location in space with no length, width, or height. A point is represented by a dot, and we usually name a point with a capital letter. For example, here is point P. • P Point P A line is a straight set of points that continues forever in two directions. When we draw a line through two points, we draw arrows at the ends to show that the line never ends. We name the line using any two points on the line and put the notation · above the letters to indicate that it is a line. We can also name a line with a lowercase · letter. For example, here is line PQ or PQ or line l. P l Q · line PQ or PQ or line l A line segment is a piece of a line with two endpoints. We name a line segment using its two endpoints. For example, this line segment with endpoints A and B can be named AB or BA. A B The name of this line segment is AB or BA. A ray is a part of a line. It has one endpoint and continues forever in the other direction. We name a ray using the endpoint fi rst and any other point on the ray. Here is ¡ ray RT, which we write as RT . R T ¡ Ray RT or RT www.mhhe.com/messersmith SECTION 4.1 Introduction to Geometry 285
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