464 CHAPTER 8 Geometry Polygons SECTION 8.2 LEARNING GOALS Upon completion of this section, you will be able to: 7 Solve problems involving the sides and angles of polygons. 7 Solve problems involving similar figures. 7 Solve problems involving congruent figures. What shape would you use to best describe each of the following road signs: a stop sign, a yield sign, a speed limit sign? In this section, we will study the shapes of these and other geometric figures that can be classified as polygons. Why This Is Important In addition to road signs, polygons and their properties are used in many applications we see in our daily lives. Polygons play an important role in the architecture of buildings, in floor tile patterns, in map making, and in many engineering applications. A basic understanding of polygons can be helpful in solving a variety of problems. a) Place one end of the compass at point A and the other end at point B and draw an arc as shown (Fig. b). b) Now turn the compass around and draw another arc as shown. Label the point of intersection of the two arcs C (Fig. c). c) Draw line segments AC and BC. This completes the construction of equilateral triangle ABC (Fig. d). a) – c) Answers will vary. A B Figure a A B Figure b C A B Figure c C A B Figure d 102. If lines l and m are parallel lines and if lines l and n are skew lines, is it true that lines m and n must also be skew? (Hint: Look at Fig. 8.5.) Explain your answer and include a sketch to support your answer. No. Line m and line n may intersect. 103. Two lines are perpendicular if they intersect at right angles. If lines l and m are perpendicular and if lines m and n are perpendicular, is it true that lines l and n must also be perpendicular? Explain your answer and include a sketch to support your answer. No. Line l and line n may be parallel or skew. 104. Suppose you have three distinct lines, all lying in the same plane. Determine all the possible ways in which the three lines can be related. There are four cases. Sketch each case. * 105. ABC and CBD are complementary and m CBD is twice the m ABC. ABD and DBE are supplementary angles. a) Draw a sketch illustrating ABC, CBD, and DBE. * b) Determine m ABC. 30° c) Determine m CBD. 60° d) Determine m DBE. 90° Research Activities 106. Euclid Write a research paper on Euclid’s contributions to geometry. 107. Classic Geometry Write a research paper on the three classic geometry problems of Greek antiquity (see the Did You Know? on page 458). 108. Geometric Constructions Research the geometric constructions that use a straightedge and a compass only. Prepare a poster demonstrating five of these basic constructions. *See Instructor Answer Appendix LightField Studios/ Shutterstock
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