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Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 Pages 6–9 Exercises 1. 80, 160 12. 1 , 1 2. 33,333; 333,333 13. James, John 3. –3, 4 14. Elizabeth, Louisa 4. 1, 1 16 32 5 6 15. Andrew, Ulysses 5. 3, 0 16. Gemini, Cancer 6. 1, 1 17. 3 20. The sum of the first 30 pos. even numbers is 30 • 31, or 930. 21. The sum of the first 100 pos. even numbers is 100 • 101, or 10,100. 7. N, T 8. J, J 19. The sum of the first 6 pos. even numbers is 6 • 7, or 42. 18. 9. 720, 5040 10. 64, 128 11. 1 , 1 36 49 1-1 Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 22. The sum of the first 100 odd numbers is 1002, or 10,000. 28. 1 ÷ 1 = 3 and 3 is 2 3 2 2 improper. 29. 75°F 25–28. Answers may vary. Samples are given. 25. 8 + (–5 = 3) and 3 >/ 8 26. 1 • 1 > 1 and 1 • 1 > 1 / / 2 3 2 3 2 3 27. –6 – (–4) < –6 and –6 – (–4) < –4 32. 10, 13 33. 0.0001, 0.00001 23. 555,555,555 24. 123,454,321 31. 31, 43 30. 40 push-ups; answers may vary. Sample: Not very confident, Dino may reach a limit to the number of push-ups he can do in his allotted time for exercises. 1-1 34. 201, 202 35. 63, 127 36. 31 , 63 32 64 37. J, S 38. CA, CO 39. B, C Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 40. Answers may vary. Sample: In Exercise 31, each number increases by increasing multiples of 2. In Exercise 33, to get the next term, divide by 10. 42. 43. 44. 41. 45. You would get a third line between and parallel to the first two lines. 46. 102 cm 1-1 47. Answers may vary. Samples are given. a. Women may soon outrun men in running competitions. b. The conclusion was based on continuing the trend shown in past records. c. The conclusions are based on fairly recent records for women, and those rates of improvement may not continue. The conclusion about the marathon is most suspect because records date only from 1955. Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 48. a. b. about 12,000 radio stations in 2010 c. Answers may vary. Sample: Confident; the pattern has held for several decades. 49. Answers may vary. Sample: 1, 3, 9, 27, 81, . . . 1, 3, 5, 7, 9, . . . 50. His conjecture is 52. probably false because most 53. people’s growth slows by 18 until they stop growing somewhere between 18 and 22 years. 51. a. b. H and I c. a circle 1-1 21, 34, 55 a. Leap years are years that are divisible by 4. b. 2020, 2100, and 2400 c. Leap years are years divisible by 4, except the final year of a century which must be divisible by 400. So, 2100 will not be a leap year, but 2400 will be. Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 54. Answers may vary. Sample: 55. (continued) d. 100 + 99 + 98 + … + 3 + 2 + 1 1 + 2 + 3 + … + 98 + 99 + 100 101 + 101 + 101 + … + 101 + 101 + 101 56. B The sum of the first 100 numbers is 57. I 100 • 101 , or 5050. 2 The sum of the first n numbers is n(n+1) . 2 55. a. 1, 3, 6, 10, 15, 21 b. They are the same. c. The diagram shows the product of n and n + 1 divided by 2 when n = 3. The result is 6. 1-1 58. [2] a. 25, 36, 49 b. n2 [1] one part correct Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 59. [4] a. The product of 11 and a three-digit number that begins and ends in 1 is a four-digit number that begins and ends in 1 and has middle digits that are each one greater than the middle digit of the three-digit number. (151)(11) = 1661 (161)(11) = 1771 59. (continued) [3] minor error in explanation 60-67. [2] incorrect description in part (a) [1] correct products for (151)(11), (161)(11), and (181)(11) 68. B b. 1991 69. N c. No; (191)(11) = 2101 70. G 1-1 Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 Find a pattern for each sequence. Use the pattern to show the next two terms or figures. Use the table and inductive reasoning. 1. 3, –6, 18, –72, 360 –2160; 15,120 2. 3. Find the sum of the first 10 counting numbers. 55 4. Find the sum of the first 1000 counting numbers. 500,500 Show that the conjecture is false by finding one counterexample. 5. The sum of two prime numbers is an even number. Sample: 2+3=5, and 5 is not even 1-1 Points, Lines, and Planes GEOMETRY LESSON 1-2 Pages 13–16 Exercises 1. no 2. yes; line n 3. yes; line n 4. yes; line m 5. yes; line n 6. no 7. no 8. yes; line m 16. BCGH 9. Answers may vary. Sample: AE, EC, GA 10. Answers may vary. Sample: BF, CD, DF 17. RS 18. VW 19. UV 11. ABCD 20. XT 12. EFHG 21. planes QUX and QUV 13. ABHF 22. planes XTS and QTS 14. EDCG 23. planes UXT and WXT 15. EFAD 24. UVW and RVW 1-2 Points, Lines, and Planes GEOMETRY LESSON 1-2 25. 27. 29. 30. S 26. 28. 31. X 32. R 33. Q 34. X 1-2 Points, Lines, and Planes GEOMETRY LESSON 1-2 35. no 36. yes 37. no 38. coplanar 39. coplanar 40. noncoplanar 41. coplanar 42. noncoplanar 44. Answers may vary. Sample: The plane of the ceiling and the plane of a wall intersect in a line. 45. Through any three noncollinear points there is exactly one plane. The ends of the legs of the tripod represent three noncollinear points, so they rest in one plane. Therefore, the tripod won’t wobble. 43. noncoplanar 1-2 46. Postulate 1-1: Through any two points there is exactly one line. 47. Answer may vary. Sample: 48. 49. not possible Points, Lines, and Planes GEOMETRY LESSON 1-2 50. 56. 54. 51. not possible 52. no no 55. 57. yes no 53. yes 58. yes yes 1-2 Points, Lines, and Planes GEOMETRY LESSON 1-2 59. 65. never yes 60. always 61. never 68. Answers may vary. Sample: 66. a. 1 b. 1 c. 1 d. 1 e. A line and a point not on the line are always coplanar. 67. Post. 1-3: If two planes intersect, then they intersect in exactly one line. 62. always 69. A, B, and D 63. always 70. Post. 1-1: Through any two points there is 64. sometimes Post. 1-4: Through three noncollinear points there is exactly one plane. 1-2 exactly one line. Points, Lines, and Planes GEOMETRY LESSON 1-2 71. Post. 1-3: If two planes intersect, then they intersect in exactly one line. 72. The end of one leg might not be coplanar with the ends of the other three legs. (Post. 1-4) 74. 76. yes no 75. 77. 73. no yes yes 1-2 Points, Lines, and Planes GEOMETRY LESSON 1-2 80. 78. no 79. Infinitely many; explanations may vary. Sample: Infinitely many planes can intersect in one line. By Post. 1-1, points D and B determine a line and points A and D determine a line. The distress signal is on both lines and, by Post. 1-2, there can be only one distress signal. 1-2 81. a. Since the plane is flat, the line would have to curve so as to contain the 2 points and not lie in the plane; but lines are straight. b. One plane; Points A, B, and C are noncollinear. By Post. 1-4, they are coplanar. Then, by part (a), AB and BC are coplanar. 82. 1 Points, Lines, and Planes GEOMETRY LESSON 1-2 83. 1 4 90. 91. I, K 84. 1 92. 42, 56 85. A 93. 1024, 4096 86. I 94. 25, –5 87. B 95. 34 88. H 96. 44 89. [2] a. ABD, ABC, ACD, BCD b. AD, BD, CD [1] one part correct The pattern 3, 9, 7, 1 repeats 11 times for n = 1 to 44. For n = 45, the last digit is 3. 1-2 Points, Lines, and Planes GEOMETRY LESSON 1-2 Use the diagram at right. 1. Name three collinear points. D, J, and H 2. Name two different planes that contain points C and G. planes BCGF and CGHD 3. Name the intersection of plane AED and plane HEG. HE 4. How many planes contain the points A, F, and H? 1 5. Show that this conjecture is false by finding one counterexample: Two planes always intersect in exactly one line. Sample: Planes AEHD and BFGC never intersect. 1-2 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 Pages 19-23 Exercises 1. 2. 7. a. TS or TR, TW b. SR, ST 12. BC 13. BE, CF 3. 8. 4; RY, SY, TY, WY 4. 9. Answers may vary. Sample: 2; YS or YR, YT or YW 15. AD, AB, AC 10. Answers may vary. Check students’ work. 17. ABC || DEF 5. RS, RT, RW, ST, SW, TW 6. RS, ST, TW, WT, TS, SR 11. DF 1-3 14. DE, EF, BE 16. BC, EF Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 18-20 Answers may vary. Samples are given 18. BE || AD 19. CF, DE 20. DEF, BC 21. FG 22. Answers may vary. Sample: CD, AB 23. BG, DH, CL 25. true 31. False; they are ||. 26. False; they are skew. 32. False; they are ||. 27. true 33. Yes; both name the segment with endpoints X and Y. 28. False; they intersect above CG. 29. true 34. No; the two rays have different endpoints. 30. False; they intersect above pt. A. 35. Yes; both are the line through pts. X and Y. 24. AF 1-3 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 41. never 36. 42. sometimes 43. always 44. sometimes 37. always 38. never 39. always 40. always 49. a. Answers may vary. Sample: northeast and southwest b. Answers may vary. Sample: northwest and southeast, east and west 50. Two lines can be parallel, skew, or intersecting in one 46. sometimes point. Sample: train tracks–parallel; vapor 47. sometimes trail of a northbound jet and an eastbound jet 48. Answers may vary. at different altitudes– Sample: (0, 0); check skew; streets that students’ graphs. cross–intersecting 45. always 1-3 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 51. Answers may vary. 55. a. The lines of Sample: Skew lines intersection are cannot be contained in parallel. one plane. Therefore, they have “escaped” a b. Examples may vary. plane. Sample: The floor and ceiling are 52. ST || UV parallel. A wall intersects both. The lines of intersection 53. Answers may vary. are parallel. Sample: XY and ZW intersect at R. 56. Answers may vary. Sample: The diamond structure makes it tough, strong, hard, and durable. The graphite structure makes it soft and slippery. 57. a. one segment; EF b. 54. Planes ABC and DCBF intersect in BC. 3 segments; EF, EG, FG 1-3 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 58. No; two different planes cannot intersect in more than one line. 57. c. 59. yes; plane P, for example Answers may vary. Sample: For each “new” point, the number of new segments equals the number of “old” points. d. 45 segments 61. QR 62. Yes; no; yes; explanations may vary. 63. D 64. H 65. B 66. F 67. B 60. Answers may vary. Sample: VR, QR, SR e. n(n – 1) 68. C 69. D 2 1-3 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 71–78. Answers may vary. 70. [2] a. Alike: They do Samples are given. not intersect. Different: Parallel 71. EF lines are coplanar and skew lines lie 72. A in different planes. 73. C b. No; of the 8 other lines shown, 4 intersect JM and 4 are skew to JM. 80. 81. 82. 1.4, 1.48 83. –22, –29 74. AEF and HEF 84. FG, GH 75. ABH 85. P, S 76. EHG 86. No; whenever you subtract a negative number, the answer is greater than the given number. Also, if you subtract 0, the answer stays the same. 77. FG [1] one likeness, one difference 79. 78. B 1-3 Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 Use the figure below for Exercises 1-3. Use the figure below for Exercises 4 and 5. 1. Name the segments that 4. Name a pair of parallel planes. form the triangle. RS, TR, ST plane BCD || plane XWQ 2. Name the rays that have point T 5. Name a line that is skew to XW. as their endpoint. TO, TP, TR, TS AC or BD 3. Explain how you can tell that no lines in the figure are parallel or skew. The three pairs of lines intersect, so they cannot be parallel or skew. 1-3 Measuring Segments and Angles GEOMETRY LESSON 1-4 Pages 29–33 Exercises 1. 9; 9; yes 9. 25 15. 130 2. 9; 6; no 10. a. 13 b. RS = 40, ST = 24 16. XYZ, ZYX, Y 17. MCP, 1 PCM, 18. ABC, CBA 19. CBD, DBC 3. 11; 13; no 4. 7; 6; no 5. XY = ZW 6. ZX = WY 11. a. 7 b. RS = 60, ST = 36, RT = 96 12. a. 9 b. 9; 18 7. YZ < XW 13. 33 8. 24 14. 34 1-4 C or Measuring Segments and Angles GEOMETRY LESSON 1-4 20-23. Drawings may vary. 20. 21. 24. 60; acute 33. –2.5, 2.5 25. 90; right 34. –3.5, 3.5 26. 135; obtuse 35. –6, –1, 1, 6 27. 34 36. a. 78 mi b. Answers may vary. Sample: measuring with a ruler 28. 70 22. 29. Q 37–41. Check students’ work. 30. 6 23. 31. –4 32. 1 1-4 Measuring Segments and Angles GEOMETRY LESSON 1-4 42. true; AB = 2, CD = 2 43. false; BD = 9, CD = 2 49. Answers may vary. Sample: (15, 0), (–9, 0), (3, 12), (3, –12) 44. false; AC = 9, BD = 9, AD = 11, and 9 + 9 =/ 11 50–54. Check students’ work. 45. true; AC = 9, CD = 2, AD = 11, and 9 + 2 = 11 56–58. Answers may vary. Samples are given. 55. about 42° 60. 150 61. 30 62. 100 63. 40 64. 80 65. 125 56. 3:00, 9:00 46. 2, 12 66. 125 57. 5:00, 7:00 47. 115 58. 6:00, 12:32 48. 65 59. 180 1-4 Measuring Segments and Angles GEOMETRY LESSON 1-4 67–68. Answers may vary. Samples are given. 67. 68. 69. QVM and MNP and MQV and VPN 71. y = 15; AC = 24, DC = 12 72. ED = 10, DB = 10, EB = 20 MVN PNQ 70. a. 19.5 b. 43; 137 c. Answers may vary. Sample: The sum of the measures should be 180. 73. a. Answers may vary. Sample: The two rays come together at a sharp point. 75. 12; m AOC = 82, m AOB = 32, m BOC = 50 76. 8; m AOB = 30, m BOC = 50, m COD = 30 77. 18; m AOB = 28, m BOC = 52, m AOD = 108 b. Answers may vary. Sample: Molly had an acute pain in her 78. 7; m AOB = 28, m BOC = 49, knee. m AOD = 111 74. 45, 75, and 165, or 135, 105, and 15 1-4 79. 30 Measuring Segments and Angles GEOMETRY LESSON 1-4 80. a–c. Check students’ 86. [2] a. work. 87. never 81. Angle Add. Post. 89. always 82. C 83. F 84. D 85. H 88. never b. An obtuse measures between 90 and 180 degrees; the least and greatest whole number values are 91 and 179 degrees. Part of ABC is 12°. So the least and greatest measures for DBC are 79 and 167. [1] one part correct 1-4 90. never 91. always 92. always 93. always 94. never 95. 25, 30 96. 3125; 15,625 97. 30, 34 Measuring Segments and Angles GEOMETRY LESSON 1-4 Use the figure below for Exercises 1-3. Use the figure below for Exercises 4–6. 1. If XT = 12 and XZ = 21, then TZ = 7. 9 2. If XZ = 3x, XT = x + 3, and TZ = 13, find XZ. 24 3. Suppose that T is the midpoint of XZ. If XT = 2x + 11 and XZ = 5x + 8, find the value of x. 14 4. Name 2 two different ways. DAB, BAD 5. Measure and classify 1, 2, and BAC. 90°, right; 30°, acute; 120°, obtuse 6. Which postulate relates the measures of 1, 2, and BAC? Angle Addition Postulate 1-4 Basic Construction GEOMETRY LESSON 1-5 Pages 37-40 Exercises 1. 9. a. 11; 30 b. 30 c. 60 6. 2. 10. 5; 50 3. 7. 11. 15; 48 12. 11; 56 4. 13. 5. 8. 1-5 Basic Construction GEOMETRY LESSON 1-5 14. 16. Find a segment on XY so that you can construct YZ as its bisector. 15. 1-5 17. Find a segment on SQ so that you can construct SP as its bisector. Then bisect PSQ. Basic Construction GEOMETRY LESSON 1-5 18. a. CBD; 41 b. 82 c. 49; 49 19. a-b. 20. Locate points A and B on a line. Then construct a at A and B as in Exercise 16. Construct AD and BC so that AB = AD = BC. 21. (continued) b. Infinitely many; there’s only 1 midpt. but there exist infinitely many lines through the midpt. A segment has exactly one bisecting line because there can be only one line 21. Explanations may vary. to a segment at its Samples are given. midpt. a. One midpt.; a midpt. divides a segment into c. There are an infinite two segments. If number of lines in there were more than space that are to a one midpt. the segment at its midpt. segments wouldn’t be . The lines are coplanar. 20. (continued) 1-5 Basic Construction GEOMETRY LESSON 1-5 22. 23. 24. 25. They are both correct. If you mult. each side of Lani’s eq. by 2, the result is Denyse’s eq. 26. Open the compass to more than half the measure of the segment. Swing large arcs from the endpts. to intersect above and below the segment. Draw a line through the two pts. where the arcs intersect. The pt. where the line and segment intersect is the midpt. of the segment. 1-5 27. 28. a. They appear to meet at one pt. Basic Construction GEOMETRY LESSON 1-5 28. (continued) b. 30. 33. a. c. The three bisectors of a intersect in one pt. 29. 31. impossible; the short segments are not long enough to form a . 32. impossible; the short segments are not long enough to form a . 1-5 b. They are all 60°. c. Answers may vary. Sample: Mark a pt., A. Swing a long arc from A. From a pt. P on the arc, swing another arc the same size that intersects the arc at a second pt., Q. Draw PAQ. To construct a 30° , bisect the 60° . Basic Construction GEOMETRY LESSON 1-5 34. a-c. 35, (continued) c. Point O is the center of the circle. 36. ; the line intersects. 37. D 38. F 35. a-b. 39. [2] a.Draw XY. With the compass pt. on B swing an arc that intersects BA and BC. Label the intersections P and Q, respectively. With the compass point on X, swing a arc intersecting XY. 1-5 39. [2] (continued) Label the intersection K. Open the compass to PQ. With compass pt. on K, swing an arc to intersect the first arc. Label the intersection R. Draw XR. Basic Construction GEOMETRY LESSON 1-5 41. 39. [2] b. With compass 40. (continued) open to XK, put 42. c. Draw AB. Do compass point on X constructions as in 43. and swing an arc parts a and b. Open 44. intersecting XR. With the compass to the 45. compass on R and length of the shortest open to KR, swing an segment in part b. arc to intersect the first With the pt. of the arc. Label intersection compass on B, swing 46. T. Draw XT. an arc in the opp. 47. [1] one part correct direction from A intersecting AB at C. 48. 40. [4] a. Construct its AC = 1.25 (AB). bisector. 49. b. Construct the bisector. [3] explanations are not Then construct the thorough 50. bisector of two new [2] two explanations correct segments. [1] part (a) correct 1-5 6 10 4 3 100 20 and 180 No; they do not have the same endpt. Yes; they both represent a segment with endpts. R and S. Basic Construction GEOMETRY LESSON 1-5 Use the figure at right. NQ bisects DNB. For problems 1-4, check students’ work. 1. Construct AC so that AC NB. 2. Construct the perpendicular bisector of AC. 3. Construct RST so that RST 4. Construct the bisector of RST. QNB. 5. Find x. 17 6. Find m DNB. 88 1-5 The Coordinate Plane GEOMETRY LESSON 1-6 Pages 46–49 Exercises 1. 6 11. about 4.5 mi 21. (6, 1) 2. 18 12. about 3.2 mi 22. (–2.25, 2.1) 3. 8 13. 6.4 23. (3 7 , –3) 4. 9 14. 15.8 24. (10, –20) 5. 23.3 15. 15.8 25. (5, –1) 6. 10 16. 5 26. (0, –34) 7. 25 17. B, C, D, E, F 27. (12, –24) 8. 12.2 18. (4, 2) 28. (9, –28) 9. 12.0 19. (3, 1) 29. (5.5, –13.5) 10. 9 mi 20. (3.5, 1) 30. (8, 18) 8 1-6 The Coordinate Plane GEOMETRY LESSON 1-6 31. (4, –11) 40. 2.2; (3.5, 1) 32. 5.0; (4.5, 4) 41. IV 33. 5.8; (1.5, 0.5) 42. 43. 34. 7.1; (–1.5, 0.5) ST = (5 – 2)2 + (–3 – (–6))2 = 9 + 9 = 3 2 4.2 TV = (6 – 5)2 + (–6 – (–3))2 = 1 + 9 = 10 3.2 35. 5.4; (–2.5, 3) 36. 10; (1, –4) 37. 2.8; (–4, –4) 38. 6.7; (–2.5, –2) 39. 5.4; (3, 0.5) The midpts. Are the same, (5, 4). The diagonals bisect each other. VW = (5 – 6)2 + (–9 – (–6))2 = 9 + 9 = 3 2 3.2 SW = (5 – 2)2 + (–9 – (–6))2 = 9+9=3 2 4.2 No, but ST = SW and TV = VW. 1-6 The Coordinate Plane GEOMETRY LESSON 1-6 44. 19.2 units; (–1.5, 0) 50. 1073 mi 45. 10.8 units; (3, –4) 51. 2693 mi 46. 5.4 units; (–1, 0.5) 52. 328 mi 47. Z; about 12 units 53–56. Answers may vary. Samples are 48. 165 units; The dist. TV given. is less than the dist. TU, so the airplane 53. (3, 6), (0, 4.5) should fly from T to V to U for the shortest 54. E (0, 0), (8, 4) route. 55. (1, 0), (–1, 4) 49. 934 mi 56. (0, 10), (5, 0) 1-6 57. exactly one pt., E (–5, 2) 58. exactly one pt., J (2, –2) 59. a–f. Answers may vary. Samples are given. a. BC = AD b. If two opp. sides of a quad. are both || and , then the other two opp. sides are . The Coordinate Plane GEOMETRY LESSON 1-6 59. (continued) c. The midpts. are the same. 59. (continued) f. If a pair of opp. sides of a quad. are both || and , then d. If one pair of opp. the segment joining sides of a quad. are the midpts. of the both || and , then other two sides has its diagonals bisect the same length as each other. each of the first pair of sides. e. EF = AB 60. A (0, 0, 0) B (6, 0, 0) C (6, –3.5, 0) D (0, –3.5, 0) E (0, 0, 9) F (6, 0, 9) G (0, –3.5, 9) 1-6 61. 62. 6.5 units 63. 11.7 units 64. B 65. I The Coordinate Plane GEOMETRY LESSON 1-6 66. A 70. 73. 71. 74. 10 67. C 68. A 69. [2] a. (–10, 8), (–1, 5), (8, 2) b. Yes, R must be (–10, 8) so that RQ = 160. 75. 10 76. 48 72. 77. TAP, 78. 150 [1] part (a) correct or plausible explanation for part (b) 1-6 PAT The Coordinate Plane GEOMETRY LESSON 1-6 A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6). 1. Find the distance between A and B to the nearest tenth. 12.4 2. Find BC to the nearest tenth. 5.4 3. Find the midpoint M of AC to the nearest tenth. (–1, 1) 4. B is the midpoint of AD. Find the coordinates of endpoint D. (–3, –16) 5. An airplane flies from Stanton to Mercury in a straight flight path. Mercury is 300 miles east and 400 miles south of Stanton. How many miles is the flight? 500 mi 6. Toni rides 2 miles north, then 5 miles west, and then 14 miles south. At the end of her ride, how far is Toni from her starting point, measured in a straight line? 13 mi 1-6 Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 Pages 55–58 Exercises 16. 1. 22 in. 9. 10 2. 36 cm 10. 3.7 3. 56 in. 11. 2 1 ft in. m 14.6 units 4. 78 cm 12. 56.5 in. 5. 120 m 13. 22.9 m 6. 48 in. 14. 1.6 yd 7. 38 ft 15. 351.9 cm 17. 8. 15 cm 25.1 units 1-7 Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 1 3 18. 20. 1 ft2 or 192 in.2 29. 9 21. 4320 in.2 or 3 yd2 30. 0.25 22. 1 1 ft2 of 162 in.2 31. 9.9225 23. 8000 cm2 or 0.8 m2 32. 0.01 64 in.2 m2 ft2 8 16 units 19. 24. 5.7 m2 or 57,000 25. 120,000 26. 6000 27. 400 ft2 cm2 cm2 or 12 m2 2 or 666 yd2 3 m2 m2 33. 153.9 ft2 34. 54.1 m2 35. 452.4 cm2 36. 452.4 in.2 37. 310 m2 38 units 28. 64 ft2 1-7 38. 19 yd2 Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 39. 24 cm2 40. 80 in.2 41. a. 144 in.2 b. 1 ft2 c. 144; a square whose sides are 12 in. long and a square whose sides are 1 ft long are the same size. 43. 3289 m2 44–47. Answers may vary. Samples are given. 44. 38 in.; 90 in.2 45. 39 in.; 93.5 in.2 48. Answers may vary. Sample: For Exercise 46, you use feet because the bulletin board is too big for inches. You do not use yards because your estimated lengths in feet were not divisible by 3. 46. 12 ft; 8 ft2 49. 16 cm 47. 8 ft; 3.75 ft2 50. 96 cm2 42. a. 30 squares b. 16; 9; 4; 1 c. They are =. Post 1-10 51. 288 cm 1-7 Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 52. a. Yes; every square is a rectangle. 54. 56. 38 units 57. 54 units2 b. Answers may vary. Sample: No, not all rectangles are squares. c. A = ( P 4 2 ) or A = P2 16 58. 1,620,000 m2 perimeter = 10 units area = 4 units2 59. 30 m 60. (4x – 2) units 55. 61. Area; the wall is a surface. 53. 512 tiles perimeter = 16 units area = 15 units2 1-7 62. Perimeter; weather stripping must fit the edges of the door. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 63. Perimeter; the fence must fit the perimeter of the garden. 64. Area; the floor is a surface. 65. 6.25 units2 66. a. base 1 2 3 24 25 26 47 48 49 height 98 96 94 : : 52 50 48 : : 6 4 2 1-7 area 98 192 282 b. 1248 1250 1248 282 192 98 c. 25 ft by 50 ft Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 67. a. b. c. d. 9 9 9 9 3a units2 20 2 69. 25a units2 4 68. 70. (9m2 – 24mn + 16n2) units2 71. Answers may vary. Sample: one 8 in.-by-8 in. square + one 5 in.by-5 in. square + two 4 in.-by-4 in. squares 72. 388.5 yd 73. 64 74. 2336 83. 9.2 units; (1, 6.5) 75. 540 84. 6.7 units; (–2.5, –2) 76. 216 85. 90 77. 810 86. WI 78. (15, 13) 87. 62 units 79. 8.5 units; (5.5, 5) 88. 18 units 80. 5.8 units; (1.5, 5.5) 89. 6 units 81. 13.9 units; (3, 5.5) 90. 33 units 82. 6.4 units; (–2, 3.5) 1-7 RI Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 A rectangle is 9 ft long and 40 in. wide. 1. Find the perimeter in inches. 296 in. 2. Find the area in square feet. 30 ft2 3. The diameter of a circle is 18 cm. Find the area in terms of . 81 cm2 4. Find the perimeter of a triangle whose vertices are X(–6, 2), Y(8, 2), and Z(3, 14). 42 units 5. Find the area of the figure below. All angles are right angles. 256 in.2 1-7 Tools of Geometry GEOMETRY CHAPTER 1 Page 64 1. Div. each preceding term by –2; 1 , – 1 2 4 2. Add 2 to the preceding term; 10, 12 4. Answers may vary. Sample: 1, 2, 4, 8, 16, 32, . . . 1, 2, 4, 7, 11, 16, . . . In the first seq. double each term. In the second seq., add consecutive counting numbers. 3. Rotate the U clockwise one-quarter turn. 5. A, B, C Alphabet is backwards; 6. Answers may vary. Sample: A, B, C, D 7. Answers may vary. Sample: A, B, D, E 8. B 9. a. b. c. d. 1 infinitely many 1 1 10. 29,054.0 ft2 11. never 12. sometimes 13. never 14. always 15. never 1-A Tools of Geometry GEOMETRY CHAPTER 1 16. 10 17. a. (11, 19) b. MC = MD = 136 18. 19.1 units 24. Answers may vary. Sample: Some ways of naming an can help identify a side or vertex. 25. 19. 800 cm2 or 0.08 m2 20. 12.25 in.2 21. 63.62 cm2 22. 7 23. 9 26. bisector 27. VW 28. 7 units 1-A 29. AY 30. E, AY 31. 33 1 yd2 3