Chapter 4: Summary Definition/Procedure Example Identify Lines, Line Segments, and Rays Space is an unlimited, three-dimensional expanse. A plane is a fl at surface that continues indefi nitely. A point is a location in space with no length, width, or height. A line is a straight set of points that continues forever in two directions. A line segment is a piece of a line with two endpoints. A ray is a part of a line that has one endpoint and that continues forever in the other direction. (p. 285) Identify each fi gure as a line, a line segment, or a ray. Then, name it using correct notation. a) R T b) Y Z c) C A Solution a) This fi gure is straight with two endpoints. This is a line segment. Write its name as RT or TR. b) This fi gure is straight and continues forever in both · directions. This is a line. Write its name as YZ · or ZY . c) This fi gure has one endpoint and an arrowhead on the other end indicating it goes on forever in that direction. This is a ray.¡ Write its name as CA . (Notice that the C must come fi rst because it is the endpoint of the ray.) Identifying Angles If we join two rays at their endpoints, we get an angle. The vertex of the angle is the common endpoint. An angle is denoted by the symbol . (p. 286) Name each of the angles in this fi gure in two different ways. A 1 3 4 2 B E D C Solution First, notice that E is the vertex of all the angles. So, we cannot use just the vertex to name any of the angles in this fi gure. We can give each of the angles the following names: 1: AEB or BEA 2: BEC or CEB 3: CED or DEC 4: DEA or AED Classifying Angles We measure the size of an angle using degrees. The symbol for degrees is . An acute angle is an angle whose measure is greater than 0 and less than 90. A right angle is an angle whose measure is 90. An obtuse angle is an angle whose measure is greater than 90 and less than 180. A straight angle is an angle whose measure is 180. (p. 288) Classify each angle as acute, right, obtuse, or straight. a) T K W b) 1 c) G F H d) V Solution a) The small square inside the angle tells us that its measure is exactly 90. KWT is a right angle. b) The measure of 1 is less than 90, so it is an acute angle. c) The measure of FGH is greater than 90 and less than 180. It is an obtuse angle. d) The measure of V is 180, so it is a straight angle. 4.1 Introduction to Geometry www.mhhe.com/messersmith CHAPTER 4 Summary 343
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