536 CHAPTER 8 Geometry Section 8.5 Rigid Motions The rigid motions: Reflections, translations, rotations, and glide reflections are defined and discussed throughout Section 8.5. Reflective symmetry, rotational symmetry, and tessellations are described in Section 8.5. Discussion, pages 501–502, Examples 1– 6, pages 502–510 Discussion, pages 510–513, Examples 7 and 8, pages 511–513 Section 8.6 Topology Möbius strip, Klein bottle, maps, Jordan curves, and topological equivalence are described in Section 8.6. Discussion, pages 520–524, Example 1 and 2, pages 523–524 Section 8.7 The Fifth Axiom Fifth axiom in Euclidean geometry: Given a line and a point not on the line, one and only one line can be drawn through the given point parallel to the given line. Fifth axiom in elliptical geometry: Given a line and a point not on the line, no line can be drawn through the given point parallel to the given line. Fifth axiom in hyperbolic geometry: Given a line and a point not on the line, two or more lines can be drawn through the given point parallel to the given line. Discussion, pages 527–530 Fractal Geometry Discussion, pages 530–532 8.1 In Exercises 1– 6, use the figure shown to determine the following. Many answers are possible. 1. h h BF BC < CBF or FBC 2. > CBF BCF BC 3. BF FC BC < < BFC Δ 4. BH HB < BH 5. g g HI EG > F{ } 6. CF CG > { } 7. m A 27.6°. = Determine the measure of the complement of A. 62.4° 8. m B 100.5°. = Determine the measure of the supplement of B. 79.5° 8.2 In Exercises 9–12, use the similar triangles ABC and A B C ′ ′ shown to determine the following. 9. The length of BC 10.2 in. 10. The length of A B′ ′ 2 in. 11. m BAC 58° 12. m ABC 92° Review Exercises CHAPTER 8 13. In the following figure, l1 and l2 are parallel lines. Determine m 1 through m 6. * 14. Determine the sum of the measures of the interior angles of an octagon. 1080° 8.3 In Exercises 15–18, determine (a) the area and (b) the perimeter of the figure. 15. a) 99 mi2 b) 40 mi A B C D E F G H I 8 in. 6 in. 888 308 4 in. 3.4 in. B C A A9 B9 1178 438 6 5 4 3 2 1 l1 l2 11 mi 9 mi *See Instructor Answer Appendix 16. a) 36 m2 b) 28 m 3 m 6 m 3 m 5 m 5 m
RkJQdWJsaXNoZXIy NjM5ODQ=