1. Patterns and Inductive Reasoning (For help, go the Skills Handbook, page 715.) GEOMETRY LESSON 1-1 Here is a list of the counting numbers: 1, 2, 3, 4, 5, . . . Some are even and some are odd. 1. Make a list of the positive even numbers. 2. Make a list of the positive odd numbers. 3. Copy and extend this list to show the first 10 perfect squares. 12 = 1, 22 = 4, 32 = 9, 42 = 16, . . . 4. Which do you think describes the square of any odd number? It is odd. It is even. 1-1

2. Patterns and Inductive Reasoning 1. Even numbers end in 0, 2, 4, 6, or 8: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, . . . 2. Odd numbers end in 1, 3, 5, 7, or 9: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, . . . 3. 1 2 = (1)(1) = 1; 2 2 = (2)(2) = 4; 3 2 = (3)(3) = 9; 4 2 = (4)(4) = 16; 5 2 = (5)(5) = 25; 6 2 = (6)(6) = 36; 7 2 = (7)(7) = 49; 8 2 = (8)(8) = 64; 9 2 = (9)(9) = 81; 10 2 = (10)(10) = 100 4. The odd squares in Exercise 3 are all odd, so the square of any odd number is odd. GEOMETRY LESSON 1-1 Solutions 1-1

3. Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 Each term is half the preceding term. So the next two terms are 48 ÷ 2 = 24 and 24 ÷ 2 = 12. 1-1 Find a pattern for the sequence. Use the pattern to show the next two terms in the sequence. 384, 192, 96, 48, …

4. Patterns and Inductive Reasoning Find the first few sums. Notice that each sum is a perfect square and that the perfect squares form a pattern. 1 3 = 1 = 1 2 = 1 2 1 3 + 2 3 = 9 = 3 2 = (1 + 2) 2 1 3 + 2 3 + 3 3 = 36 = 6 2 = (1 + 2 + 3) 2 1 3 + 2 3 + 3 3 + 4 3 = 100 = 10 2 = (1 + 2 + 3 + 4) 2 1 3 + 2 3 + 3 3 + 4 3 + 5 3 = 225 = 15 2 = (1 + 2 + 3 + 4 + 5) 2 The sum of the first two cubes equals the square of the sum of the first two counting numbers. GEOMETRY LESSON 1-1 1-1 Make a conjecture about the sum of the cubes of the first 25 counting numbers.

5. Patterns and Inductive Reasoning GEOMETRY LESSON 1-1 This pattern continues for the fourth and fifth rows of the table. 1 3 + 2 3 + 3 3 + 4 3 = 100 = 10 2 = (1 + 2 + 3 + 4) 2 1 3 + 2 3 + 3 3 + 4 3 + 5 3 = 225 = 15 2 = (1 + 2 + 3 + 4 + 5) 2 So a conjecture might be that the sum of the cubes of the first 25 counting numbers equals the square of the sum of the first 25 counting numbers, or (1 + 2 + 3 + … + 25) 2 . 1-1 The sum of the first three cubes equals the square of the sum of the first three counting numbers. (continued)

6. Patterns and Inductive Reasoning The fourth prime number is 11. One pattern of the sequence is that each term equals the preceding term plus 2. So a possible conjecture is that the fourth prime number is 7 + 2 = 9. However, because 3 X 3 = 9 and 9 is not a prime number, this conjecture is false. GEOMETRY LESSON 1-1 1-1 The first three odd prime numbers are 3, 5, and 7. Make and test a conjecture about the fourth odd prime number.

7. Patterns and Inductive Reasoning Each year the price increased by $1.50. A possible conjecture is that the price in 2003 will increase by $1.50. If so, the price in 2003 would be $11.00 + $1.50 = $12.50. GEOMETRY LESSON 1-1 1-1 The price of overnight shipping was $8.00 in 2000, $9.50 in 2001, and $11.00 in 2002. Make a conjecture about the price in 2003. Write the data in a table. Find a pattern. 2000 $8.00 2001 2002 $9.50 $11.00

8. Patterns and Inductive Reasoning GEOMETRY LESSON 1–1 pages 6–9 Practice and Problem Solving 1. 80, 160 2. 33,333; 333,333 3. –3, 4 4. , 5. 3, 0 6. 1, 7. N, T 8. J, J 9. 720, 5040 10. 64, 128 11. , 1 16 1 32 1 36 1 49 19. The sum of the first 6 pos. even numbers is 6•7, or 42. 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. 1-1 12. , 13. James, John 14. Elizabeth, Louisa 15. Andrew, Ulysses 16. Gemini, Cancer 17. 18. 1 5 1 6

9. Patterns and Inductive Reasoning GEOMETRY LESSON 1–1 22. The sum of the first 100 odd numbers is 1002, or 10,000. 23. 555,555,555 24. 123,454,321 25–28. Answers may vary. Samples are given. 25. 8 + (–5 = 3) and 3 > 8 26. • > and • > 27. –6 – (–4) Ò –6 and – 6 – (–4) Ò –4 28. ÷ = and is improper. 29. 758F 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. 31. 31, 43 32. 10, 13 33. 0.0001, 0.00001 34. 201, 202 35. 63, 127 36. , 37. J, S 38. CA, CO 39. B, C 1 3 1 2 1 3 1 3 1 2 1 2 / / / 1 2 1 3 3 2 3 2 31 32 63 64 1-1

10. 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. 41. You would get a third line between and parallel to the first two lines. 42. 43. 44. 45. 46. 102 cm 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. 1-1

11. 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 probably false because most 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 52. 21, 34, 55 53. 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. 1-1

12. Patterns and Inductive Reasoning GEOMETRY LESSON 1–1 54. Answers may vary. Sample: 100 + 99 + 98 + … + 3 + 2 + 1 1 + 2 + 3 + … + 98 + 99 + 100 101 + 101 + 101 + … + 101 + 101 + 101 The sum of the first 100 numbers is , or 5050. The sum of the first n numbers is . 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. 100 • 101 2 n(n+1) 2 d. 56. B 57. I 58. [2] a. 25, 36, 49 b. n 2 [1] one part correct 1-1

13. 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 b. 1991 c. No; (191)(11) = 2101 [3] minor error in explanation [2] incorrect description in part ( a ) [1] correct products for (151)(11), (161)(11), and (181)(11) 60-67. 68. B 69. N 70. G 1-1

14. 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. 1. 3, –6, 18, –72, 360 2. Use the table and inductive reasoning. Make a conjecture about each value. 3. the sum of the first 10 counting numbers 4. the sum of the first 1000 counting numbers Show that the conjecture is false by finding one counterexample. 5. The sum of two prime numbers is an even number. – 2160; 15,120 55 500,500 Sample: 2+3=5, and 5 is not even 1-1

15. Points, Lines, and Planes (For help, go to the Skills Handbook, page 722.) Solve each system of equations. 1. y = x + 5 2. y = 2 x – 4 3. y = 2 x y = – x + 7 y = 4 x – 10 y = – x + 15 4. Copy the diagram of the four points A , B , C , and D . Draw as many different lines as you can to connect pairs of points. GEOMETRY LESSON 1-2 1-2

16. Points, Lines, and Planes Solutions GEOMETRY LESSON 1-2 1-2 1. By substitution, x + 5 = – x + 7; adding x – 5 to both sides results in 2 x = 2; dividing both sides by 2 results in x = 1. Since x = 1, y = (1) + 5 = 6. ( x , y ) = (1, 6) 2. By substitution, 2 x – 4 = 4 x – 10; adding –4 x + 4 to both sides results in –2 x = –6; dividing both sides by –2 results in x = 3. Since x = 3, y = 2(3) – 4 = 6 – 4 = 2. ( x , y ) = (3, 2) 3. By substitution, 2 x = – x + 15; adding x to both sides results in 3 x = 15; dividing both sides by 3 results in x = 5. Since x = 5, y = 2(5) = 10. ( x , y ) = (5, 10) 4. The 6 different lines are AB , AC , AD , BC , BD , and CD .

17. Points, Lines, and Planes Any other set of three points do not lie on a line, so no other set of three points is collinear. For example, X , Y , and Z and X , W , and Z form triangles and are not collinear. GEOMETRY LESSON 1-2 1-2 In the figure below, name three points that are collinear and three points that are not collinear. Points Y , Z , and W lie on a line, so they are collinear.

18. Points, Lines, and Planes You can name a plane using any three or more points on that plane that are not collinear. Some possible names for the plane shown are the following: plane RST plane RSU plane RTU plane STU plane RSTU GEOMETRY LESSON 1-2 1-2 Name the plane shown in two different ways.

19. Points, Lines, and Planes GEOMETRY LESSON 1-2 As you look at the cube, the front face is on plane AEFB , the back face is on plane HGC , and the left face is on plane AED . 1-2 The back and left faces of the cube intersect at HD . Planes HGC and AED intersect vertically at HD . Use the diagram below. What is the intersection of plane HGC and plane AED ?

20. Points, Lines, and Planes GEOMETRY LESSON 1-2 1-2 Points X , Y , and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by X , Y , and Z . Shade the plane that contains X , Y , and Z .

21. Points, Lines, and Planes GEOMETRY LESSON 1–2 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 pages 13–16 Practice and Problem Solving 9. Answers may vary. Sample: AE , EC , GA 10. Answers may vary. Sample: BF , CD , DF 11. ABCD 12. EFHG 13. ABHF 14. EDCG 15. EFAD 16. BCGH 17. RS 18. VW 19. UV 20. XT 21. planes QUX and QUV 22. planes XTS and QTS 23. planes UXT and WXT 24. UVW and RVW 1-2

22. Points, Lines, and Planes GEOMETRY LESSON 1–2 25. 26. 27. 28. 29. 30. S 31. X 32. R 33. Q 34. X 1-2

23. Points, Lines, and Planes 46. Postulate 1-1: Through any two points there is exactly one line. 47. Answer may vary. Sample: 48. 49. not possible GEOMETRY LESSON 1–2 35. no 36. yes 37. no 38. coplanar 39. coplanar 40. noncoplanar 41. coplanar 42. noncoplanar 43. 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. 1-2

24. Points, Lines, and Planes 50. 51. not possible 52. yes 53. yes GEOMETRY LESSON 1–2 56. no 57. no 58. yes 54. no 55. yes 1-2

25. Points, Lines, and Planes GEOMETRY LESSON 1–2 68. Answers may vary. Sample: Post. 1-3: If two planes intersect, then they intersect in exactly one line. 69. A, B, and D 70. Post. 1-1: Through any two points there is exactly one line. 59. yes 60. always 61. never 62. always 63. always 64. sometimes 65. never 66. a. 1 b. 1 c. 1 d. 1 e. A line and a point not on the line are always coplanar. 67. Post. 1-4: Through three noncollinear points there is exactly one plane. 1-2

26. Points, Lines, and Planes 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) 73. yes GEOMETRY LESSON 1–2 76. no 77. yes 74. yes 75. no 1-2

27. Points, Lines, and Planes GEOMETRY LESSON 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 78. no 79. Infinitely many; explanations may vary. Sample: Infinitely many planes can intersect in one line. 80. 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

28. Points, Lines, and Planes GEOMETRY LESSON 1–2 94. 25, -5 95. 34 96. 44 83. 84. 1 85. A 86. I 87. B 88. H 89. [2] a. ABD , ABC , ACD , BCD b. AD , BD , CD [1] one part correct 90. 91. I , K 92. 42, 56 93. 1024, 4096 1 4 1-2

29. Points, Lines, and Planes GEOMETRY LESSON 1-2 1. Name three collinear points. 2. Name two different planes that contain points C and G . 3. Name the intersection of plane AED and plane HEG . 4. How many planes contain the points A , F , and H ? 5. Show that this conjecture is false by finding one counterexample: Two planes always intersect in exactly one line. Use the diagram at right. D , J , and H planes BCGF and CGHD 1 Sample: Planes AEHD and BFGC never intersect. 1-2 HE

30. Segments, Rays, Parallel Lines and Planes (For help, go to Lesson 1-2.) Judging by appearances, will the lines intersect? 1. 2. 3. Name the plane represented by each surface of the box. 4. the bottom 5. the top 6. the front 7. the back 8. the left side 9. the right side GEOMETRY LESSON 1-3 1-3

31. Segments, Rays, Parallel Lines and Planes 1. no 2. yes 3. no 4. NMR 5. PQL 6. NKL 7. PQR 8. PKN 9. LQR GEOMETRY LESSON 1-3 Solutions 1-3

32. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 1-3 Name the segments and rays in the figure. The labeled points in the figure are A , B , and C . A segment is a part of a line consisting of two endpoints and all points between them. A segment is named by its two endpoints. So the segments are BA (or AB ) and BC (or CB ). A ray is a part of a line consisting of one endpoint and all the points of the line on one side of that endpoint. A ray is named by its endpoint first, followed by any other point on the ray. So the rays are BA and BC .

33. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 1-3 Use the figure below. Name all segments that are parallel to AE . Name all segments that are skew to AE . Parallel segments lie in the same plane, and the lines that contain them do not intersect. The three segments in the figure above that are parallel to AE are BF , CG , and DH . Skew lines are lines that do not lie in the same plane. The four lines in the figure that do not lie in the same plane as are AE , BC , CD , and GH .

34. Segments, Rays, Parallel Lines and Planes Planes are parallel if they do not intersect. If the walls of your classroom are vertical, opposite walls are parts of parallel planes. If the ceiling and floor of the classroom are level, they are parts of parallel planes. GEOMETRY LESSON 1-3 1-3 Identify a pair of parallel planes in your classroom.

35. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1–3 12. BC 13. BE , CF 14. DE , EF , BE 15. AD , AB , AC 16. BC , EF 17. ABC || DEF 1. 2. 3. 4. 5. RS , RT , RW , ST , SW , TW 6. RS , ST , TW , WT , TS , SR 7. a. TS or TR , TW b. SR , ST 8. 4; RY , SY , TY , WY 9. Answers may vary. Sample: 2; YS or YR , YT or YW 10. Answers may vary. Check students’ work. 11. DF Pages 19-22 Practice and Problem Solving 1-3

36. Segments, Rays, Parallel Lines and Planes 25. true 26. False; they are skew. 27. true 28. False; they intersect above CG . 29. true 30. False; they intersect above pt. A . GEOMETRY LESSON 1–3 31. False; they are ||. 32. False; they are ||. 33. Yes; both name the segment with endpoints X and Y . 34. No; the two rays have different endpoints. 35. Yes; both are the line through pts. X and Y . 18. BE || AD 19. CF , DE 20. DEF , BC 21 . FG 22. Answers may vary. Sample: CD , AB 23. BG , DH , CL 24. AF Pages 18-20 Answers may vary. Samples are given 1-3

37. Segments, Rays, Parallel Lines and Planes Pages 19-22 Exercises 36. 37. always 38. never 39. always 40. always GEOMETRY LESSON 1–3 41. never 42. sometimes 43. always 44. sometimes 45. always 46. sometimes 47. sometimes 48. Answers may vary. Sample: (0, 0); check students’ graphs. 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 point. Sample: train tracks–parallel; vapor trail of a northbound jet and an eastbound jet at different altitudes– skew; streets that cross–intersecting 1-3

38. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1–3 55. a. The lines of intersection are parallel. b. Examples may vary. Sample: The floor and ceiling are parallel. A wall intersects both. The lines of intersection are parallel. 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. 3 segments; EF , EG , FG 51. Answers may vary. Sample: Skew lines cannot be contained in one plane. Therefore, they have “escaped” a plane. 52. ST || UV 53. Answers may vary. Sample: XY and ZW intersect in R . 54. Planes ABC and DCBF intersect in BC . 1-3

39. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1–3 58. No; two different planes cannot intersect in more than one line. 59. yes; plane P , for example 60. Answers may vary. Sample: VR , QR , SR 61. QR 62. Yes; no; yes; explanations may vary. 63. D 64. H 65. B 66. F 67. B 68. C 69. D 57. c. Answers may vary. Sample: For each “new” point, the number of new segments equals the number of “old” points. d. 45 segments e. n(n - 1) 2 1-3

40. Segments, Rays, Parallel Lines and Planes 79. 80. 81. 82. 1.4, 1.48 83. –22, –29 84. FG , GH 85. P , S 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. GEOMETRY LESSON 1–3 71–78. Answers may vary. Samples are given. 71. EF 72. A 73. C 74. AEF and HEF 75. ABH 76. EHG 77. FG 78. B 70. [2] a. Alike: They do not intersect. Different: Parallel lines are coplanar and skew lines lie in different planes. b. No; of the 8 other lines shown, 4 intersect JM and 4 are skew to JM . [1] one likeness, one difference 1-3

41. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-3 Use the figure below for Exercises 1-3. 1. Name the segments that form the triangle. 2. Name the rays that have point T as their endpoint. 3. Explain how you can tell that no lines in the figure are parallel or skew. Use the figure below for Exercises 4 and 5. 4. Name a pair of parallel planes. 5. Name a line that is skew to XW . The three pairs of lines intersect, So they cannot be parallel or skew. plane BCD || plane XWQ 1-3 TO, TP, TR, TS AC or BD RS, TR, ST

42. Measuring Segments and Angles (For help, go to the Skills Handbook pages 719 and 720.) Simplify each absolute value expression. 1. |–6| 2. |3.5| 3. |7 – 10| 4. |–4 – 2| 5. |–2 – (–4)| 6. |–3 + 12| Solve each equation. 7. x + 2 x – 6 = 6 8. 3 x + 9 + 5 x = 81 9. w – 2 = –4 + 7 w 1-4 GEOMETRY LESSON 1-4

43. Measuring Segments and Angles GEOMETRY LESSON 1-4 Solutions 1-4 1. The number of units from 0 to –6 on the number line is 6. 2. The number of units from 0 to 3.5 on the number line is 3.5. 3. |7 – 10| = |–3|, and the number of units from 0 to –3 on the number line is 3. 4. |–4 – 2| = |–6|, and the number of units from 0 to –6 on the number line is 6. 5. |–2 – (–4)| = |–2 + 4| = |2|, and the number of units from 0 to 2 on the number line is 2. 6. |–3 + 12| = |9|, and the number of units from 0 to 9 on the number line is 9. 7. Combine like terms: 3 x – 6 = 6; add 6: 3 x = 12; divide by 3: x = 4 8. Combine like terms: 8 x + 9 = 81; subtract 9: 8 x = 72; divide by 8: x = 9 9. Add –7 w + 2: –6 w = –2; divide by –6: w = 1 3

44. Measuring Segments and Angles Use the Ruler Postulate to find the length of each segment. XY = | –5 – (–1)| = | –4| = 4 ZY = | 2 – (–1)| = |3| = 3 ZW = | 2 – 6| = |–4| = 4 GEOMETRY LESSON 1-4 1-4 Find which two of the segments XY , ZY , and ZW are congruent. Because XY = ZW , XY ZW .

45. Measuring Segments and Angles GEOMETRY LESSON 1-4 Use the Segment Addition Postulate to write an equation. AN + NB = AB Segment Addition Postulate ( 2 x – 6 ) + ( x + 7 ) = 25 Substitute. 3 x + 1 = 25 Simplify the left side. 3 x = 24 Subtract 1 from each side. x = 8 Divide each side by 3. AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25. 1-4 If AB = 25, find the value of x . Then find AN and NB . AN = 2 x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x .

46. Measuring Segments and Angles GEOMETRY LESSON 1-4 Use the definition of midpoint to write an equation. RT = RM + MT = 168 1-4 RM = MT Definition of midpoint 5 x + 9 = 8 x – 36 Substitute. 5 x + 45 = 8 x Add 36 to each side. 45 = 3 x Subtract 5 x from each side. 15 = x Divide each side by 3. RM and MT are each 84, which is half of 168, the length of RT . M is the midpoint of RT . Find RM , MT , and RT . RM = 5 x + 9 = 5( 15 ) + 9 = 84 MT = 8 x – 36 = 8( 15 ) – 36 = 84 Substitute 15 for x .

47. Measuring Segments and Angles GEOMETRY LESSON 1-4 1-4 Name the angle below in four ways. The name can be the vertex of the angle: G . Finally, the name can be a point on one side , the vertex , and a point on the other side of the angle : AGC , CGA . The name can be the number between the sides of the angle: 3 .

48. Measuring Segments and Angles GEOMETRY LESSON 1-4 1-4 Because 0 < 80 < 90, 2 is acute. m 2 = 80 Use a protractor to measure each angle. m 1 = 110 Because 90 < 110 < 180, 1 is obtuse. Find the measure of each angle. Classify each as acute , right , obtuse , or straight .

49. Measuring Segments and Angles Use the Angle Addition Postulate to solve. GEOMETRY LESSON 1-4 1-4 m 1 + m 2 = m ABC Angle Addition Postulate. 42 + m 2 = 88 Substitute 42 for m 1 and 88 for m ABC . m 2 = 46 Subtract 42 from each side. Suppose that m 1 = 42 and m ABC =88. Find m 2.

50. Measuring Segments and Angles GEOMETRY LESSON 1–4 15. 130 16. XYZ , ZYX , Y 17. MCP , PCM , C or 1 18. ABC , CBA 19. CBD , DBC 9. 25 10. a. 13 b. RS = 40, ST = 24 11. a. 7 b. RS = 60, ST = 36, RT = 96 12. a. 9 b. 9; 18 13. 33 14. 34 1. 9; 9; yes 2. 9; 6; no 3. 11; 13; no 4. 7; 6; no 5. XY = ZW 6. ZX = WY 7. YZ < XW 8. 24 pages 29–33 Practice and Problem Solving 1-4

51. Measuring Segments and Angles 20-23. Drawings may vary. 20. 21. 22. 23. GEOMETRY LESSON 1–4 33. –2.5, 2.5 34. –3.5, 3.5 35. –6, –1, 1, 6 36. a. 78 mi b. Answers may vary. Sample: measuring with a ruler 37–41. Check students’ work. 24. 60; acute 25. 90; right 26. 135; obtuse 27. 34 28. 70 29. Q 30. 6 31. –4 32. 1 1-4

52. Measuring Segments and Angles GEOMETRY LESSON 1–4 60. 150 61. 30 62. 100 63. 40 64. 80 65. 125 66. 125 49. Answers may vary. Sample: (15, 0), (–9, 0), (3, 12), (3, –12) 50–54. Check students’ work. 55. about 42° 56–58. Answers may vary. Samples are given. 56. 3:00, 9:00 57. 5:00, 7:00 58. 6:00, 12:32 59. 180 42. true; AB = 2, CD = 2 43. false; BD = 9, CD = 2 44. false; AC = 9, BD = 9, AD = 11, and 9 + 9 ≠ 11 45. true; AC = 9, CD = 2, AD = 11, and 9 + 2 = 11 46. 2, 12 47. 115 48. 65 1-4

53. Measuring Segments and Angles GEOMETRY LESSON 1–4 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 78. 7; m AOB = 28, m BOC = 49, m AOD = 111 79. 30 71. y = 15; AC = 24, DC = 12 72. ED = 10, DB = 10, EB = 20 73. a. Answers may vary. Sample: The two rays come together at a sharp point. b. Answers may vary. Sample: Molly had an acute pain in her knee. 74. 45, 75, and 165, or 135, 105, and 15 67–68. Answers may vary. Samples are given 67. QVM and VPN 68. MNP and MVN 69. MQV and PNQ 70. a. 19.5 b. 43; 137 c. Answers may vary. Sample: The sum of the measures should be 180. 1-4

54. Measuring Segments and Angles 86. [2] a. 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 GEOMETRY LESSON 1–4 87. never 88. never 89. always 90. never 91. always 92. always 93. always 94. never 95. 25, 30 96. 3125; 15,625 97. 30, 34 80. a–c. Check students’ work. 81. Angle Add. Post. 82. C 83. F 84. D 85. H 1-4

55. Measuring Segments and Angles GEOMETRY LESSON 1-4 Use the figure below for Exercises 4–6. 4. Name 2 two different ways. 5. Measure and classify 1, 2, and BAC . 6. Which postulate relates the measures of 1, 2, and BAC ? 14 Angle Addition Postulate Use the figure below for Exercises 1-3. 1. If XT = 12 and XZ = 21, then TZ = 7. 2. If XZ = 3 x , XT = x + 3, and TZ = 13, find XZ . 3. Suppose that T is the midpoint of XZ . If XT = 2 x + 11 and XZ = 5 x + 8, find the value of x . 9 24 90°, right; 30°, acute; 120°, obtuse 1-4 DAB, BAD

56. Basic Construction (For help, go to Lesson 1-3 and 1-4.) GEOMETRY LESSON 1-5 1-5 In Exercises 1-6, sketch each figure. 1. CD 2. GH 3. AB 4. line m 5. acute ABC 6. XY || ST 7. DE = 20. Point C is the midpoint of DE . Find CE . 8. Use a protractor to draw a 60° angle. 9. Use a protractor to draw a 120° angle.

57. Basic Construction GEOMETRY LESSON 1-5 Solutions 1-5 1. The figure is a segment whose endpoints are C and D . 2. The figure is a ray whose endpoint is G . 3. The figure is a line going through the points A and B . 4. 5. The figure is an angle whose measure is between 0° and 90°. 6. The figure is two segments in a plane whose corresponding lines do not intersect. 7. Since C is a midpoint, CD = CE ; also, CD + CE = 20; substituting results in CE + CE = 20, or 2 CE = 20, so CE = 10. 8. 9.

58. Basic Construction GEOMETRY LESSON 1-5 1-5 Step 2 : Open the compass to the length of KM . Construct TW congruent to KM . Step 1 : Draw a ray with endpoint T . Step 3 : With the same compass setting, put the compass point on point T . Draw an arc that intersects the ray. Label the point of intersection W . TW KM

59. Basic Construction ~ GEOMETRY LESSON 1-5 1-5 Step 3: With the same compass setting, put the compass point on point Y . Draw an arc that intersects the ray. Label the point of intersection Z . Construct Y so that Y = G . Step 1: Draw a ray with endpoint Y . Step 2: With the compass point on point G , draw an arc that intersects both sides of G . Label the points of intersection E and F .

60. Basic Construction GEOMETRY LESSON 1-5 Step 5 : Draw to complete Y . 1-5 (continued) Step 4 : Open the compass to the length EF . Keeping the same compass setting, put the compass point on Z . Draw an arc that intersects the arc you drew in Step 3. Label the point of intersection X . Y G

61. Basic Construction GEOMETRY LESSON 1-5 Without two points of intersection, no line can be drawn, so the perpendicular bisector cannot be drawn. 1-5 Step 1 : Put the compass point on point A and draw a short arc. Make sure that the opening is less than AB . 1 2 Start with AB . Step 2 : With the same compass setting, put the compass point on point B and draw a short arc. Use a compass opening less than AB . Explain why the construction of the perpendicular bisector of AB is not possible. 1 2

62. Basic Construction GEOMETRY LESSON 1-5 – 3 x = –48 Subtract 4 x from each side. x = 16 Divide each side by –3. 1-5 m AWR = m BWR Definition of angle bisector x = 4 x – 48 Substitute x for m AWR and 4 x – 48 for m BWR . m AWB = m AWR + m BWR Angle Addition Postulate m AWB = 16 + 16 = 32 Substitute 16 for m AWR and for m BWR . Draw and label a figure to illustrate the problem WR bisects AWB . m AWR = x and m BWR = 4 x – 48. Find m AWB . m AWR = 16 m BWR = 4( 16 ) – 48 = 16 Substitute 16 for x .

63. Basic Construction GEOMETRY LESSON 1-5 1-5 Step 1: Put the compass point on vertex M . Draw an arc that intersects both sides of M . Label the points of intersection B and C . Step 2: Put the compass point on point B . Draw an arc in the interior of M . Construct MX , the bisector of M .

64. Basic Construction GEOMETRY LESSON 1-5 1-5 Step 4: Draw MX . MX is the angle bisector of M . (continued) Step 3: Put the compass point on point C . Using the same compass setting, draw an arc in the interior of M . Make sure that the arcs intersect. Label the point where the two arcs intersect X .

65. Basic Construction 6. 7. 8. GEOMETRY LESSON 1–5 9. a. 11; 30 b. 30 c. 60 10. 5; 50 11. 15; 48 12. 11; 56 13. 1. 2. 3. 4. 5. 1-5

66. Basic Construction GEOMETRY LESSON 1–5 16. Find a segment on XY so that you can construct YZ as its bisector. 17. Find a segment on SQ so that you can construct SP as its bisector. Then bisect PSQ. 18. a. CBD; 41 b. 82 c. 49; 49 19. a-b. 14. 15. 1-5

67. Basic Construction GEOMETRY LESSON 1–5 21. Explanations may vary. Samples are given. a. One midpt.; a midpt. divides a segment into two segments. If there were more than one midpt. the segments wouldn’t be . 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 to a segment at its midpt. c. There are an infinite number of lines in space that are to a segment at its midpt. The lines are coplanar. 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 . 1-5

68. Basic Construction 27. 28. a. They appear to meet at one pt. GEOMETRY LESSON 1–5 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. 22. 23. 24. 1-5

69. Basic Construction 33. a. 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° . GEOMETRY LESSON 1–5 30. 31. impossible; the short segments are not long enough to form a . 32. impossible; the short segments are not long enough to form a . b. c. The three bisectors of a intersect in one pt. 29. 1-5

70. Basic Construction GEOMETRY LESSON 1–5 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 . c. Point O is the center of the circle. 36. ; the line intersects. 37. D 38. F 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 . 34. a-c. 35. a-c. 1-5

71. Basic Construction 41. 6 42. 10 43. 4 44. 3 45. 46. 100 47. 20 and 180 48. 49. No; they do not have the same endpt. 50. Yes; they both represent a segment with endpts. R and S . GEOMETRY LESSON 1–5 c. Draw AB . Do constructions as in parts a and b . Open the compass to the length of the shortest segment in part b . With the pt. of the compass on B , swing an arc in the opp. direction from A intersecting AB at C . AC = 1.25 ( AB ). [3] explanations are not thorough [2] two explanations correct [1] part (a) correct 1-5 39. [2] b. With compass open to XK, put compass point on X and swing an arc intersecting XR. With compass on R and open to KR, swing an arc to intersect the first arc. Label intersection T. Draw XT. [1] one part correct 40. [4] a. Construct its bisector. b. Construct the bisector. Then construct the bisector of two new segments.

72. Basic Construction GEOMETRY LESSON 1-5 For problems 1-4, check students’ work. QN bisects DNB . 1. Construct AC so that AC NB . 2. Construct the perpendicular bisector of AC . 3. Construct RST so that RST QNB . 4. Construct the bisector of RST . 5. Find x . 6. Find m DNB . 88 Use the figure at right. 17 1-5

73. The Coordinate Plane (For help, go to the Skills Handbook pages 715 and 716.) GEOMETRY LESSON 1-6 1-6 Find the square root of each number to the nearest tenth. Use a calculator if necessary. 1. 25 2. 17 3. 123 Evaluate each expression for m = –3 and n = 7. 4. ( m – n ) 2 5. ( n – m ) 2 6. m 2 + n 2 Evaluate each expression for a = 6 and b = –8. 7. ( a – b ) 2 8. 9. a + b 2 a 2 + b 2

74. The Coordinate Plane GEOMETRY LESSON 1-6 Solutions 1. 25 = 5 2 = 5 3. 123 11.09 2 = 11.09 4. ( m – n ) 2 = (–3 –7) 2 = (–10) 2 = 100 5. ( n – m ) 2 = –7 – (–3)) 2 = (7 + 3) 2 =10 2 = 100 6. m 2 + n 2 = (–3) 2 + (7) 2 = 9 + 49 = 58 7. ( a – b ) 2 = (6 – (–8)) 2 = (6 + 8) 2 =14 2 = 196 1-6 2. 17 4.123 2 = 4.123 8. a 2 + b 2 = (6) 2 + (–8) 2 = 36 + 64 = 100 = 10 9. – 2 2 = = –1 a + b 2 6 + (–8) 2 =

75. The Coordinate Plane Let ( x 1 , y 1 ) be the point R ( –2 , –6 ) and ( x 2 , y 2 ) be the point S ( 6 , –2 ). To the nearest tenth, RS = 11.3. GEOMETRY LESSON 1-6 1-6 d = 8 2 + (–8) 2 Simplify. Find the distance between R (–2, –6) and S (6, –2) to the nearest tenth. 128 11.3137085 Use a calculator. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 Use the Distance Formula. d = ( 6 – ( –2 )) 2 + ( –2 – ( –6 )) 2 Substitute. d = 64 + 64 = 128

76. The Coordinate Plane Oak has coordinates ( –1 , –2 ). Let ( x 1 , y 1 ) represent Oak. Symphony has coordinates ( 1 , 2 ). Let ( x 2 , y 2 ) represent Symphony. To the nearest tenth, the subway ride from Oak to Symphony is 4.5 miles. GEOMETRY LESSON 1-6 1-6 20 4.472135955 Use a calculator. d = 2 2 + 4 2 Simplify. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 Use the Distance Formula. How far is the subway ride from Oak to Symphony? Round to the nearest tenth. d = ( 1 – ( –1 )) 2 + ( 2 – ( –2 )) 2 Substitute. d = 4 + 16 = 20

77. The Coordinate Plane GEOMETRY LESSON 1-6 Use the Midpoint Formula. Let ( x 1 , y 1 ) be A ( 8 , 9 ) and ( x 2 , y 2 ) be B ( –6 , –3 ). The coordinates of midpoint M are (1, 3). 1-6 AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M . The midpoint has coordinates Midpoint Formula ( , ) x 1 + x 2 2 y 1 + y 2 2 Substitute 8 for x 1 and (–6) for x 2 . Simplify. 8 + ( –6 ) 2 The x –coordinate is = = 1 2 2 Substitute 9 for y 1 and (–3) for y 2 . Simplify. 9 + ( –3 ) 2 The y –coordinate is = = 3 6 2

78. The Coordinate Plane GEOMETRY LESSON 1-6 Find the x –coordinate of G . Find the y –coordinate of G . The coordinates of G are (–3, 6). 1-6 4 + y 2 2 5 = 1 + x 2 2 – 1 = Use the Midpoint Formula. The midpoint of DG is M (–1, 5). One endpoint is D (1, 4). Find the coordinates of the other endpoint G . – 2 = 1 + x 2 10 = 4 + y 2 Multiply each side by 2. Use the Midpoint Formula. Let ( x 1 , y 1 ) be D( 1 , 4 ) and the midpoint be ( –1 , 5 ). Solve for x 2 and y 2 , the coordinates of G . ( , ) x 1 + x 2 2 y 1 + y 2 2

79. The Coordinate Plane GEOMETRY LESSON 1–6 11. about 4.5 mi 12. about 3.2 mi 13. 6.4 14. 15.8 15. 15.8 16. 5 17. B , C , D , E , F 18. (4, 2) 19. (3, 1) 20. (3.5, 1) 21. (6, 1) 22. (–2.25, 2.1) 23. (3 , –3) 24. (10, –20) 25. (5, –1) 26. (0, –34) 27. (12, –24) 28. (9, –28) 29. (5.5, –13.5) 30. (8, 18) 31. (4, –11) 1. 6 2. 18 3. 8 4. 9 5. 23.3 6. 10 7. 25 8. 12.2 9. 12.0 10. 9 mi pages 46–48 Practice and Problem Solving 7 8 1-6

80. The Coordinate Plane GEOMETRY LESSON 1–6 41. IV 42. The midpts. Are the same, (5, 4). The diagonals bisect each other. 32. 5.0; (4.5, 4) 33. 5.8; (1.5, 0.5) 34. 7.1; (–1.5, 0.5) 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) 40. 2.2; (3.5, 1) 43. 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 SW = (5 – 6) 2 + (–9 – (–6)) 2 = 9 + 9 = 3 2 4.2 No, but ST = SW and TV = VW . 1-6

81. The Coordinate Plane GEOMETRY LESSON 1–6 50. 1073 mi 51. 2693 mi 52. 328 mi 53–56. Answers may vary. Samples are given. 53. (3, 6), (0, 4.5) 54. E (0, 0), (8, 4) 55. (1, 0), (–1, 4) 56. (0, 10), (5, 0) 44. 19.2 units; (–1.5, 0) 45. 10.8 units; (3, –4) 46. 5.4 units; (–1, 0.5) 47. Z ; about 12 units 48. 165 units; The dist. TV is less than the dist. TU , so the airplane should fly from T to V to U for the shortest route. 49. 934 mi 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 . 1-6

82. The Coordinate Plane GEOMETRY LESSON 1–6 f. If a pair of opp. sides of a quad. are both || and , then the segment joining the midpts. of the other two sides has the same length as each of the first pair of sides. 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) c. The midpts. are the same. d. If one pair of opp. sides of a quad. are both || and , then its diagonals bisect each other. e. EF = AB 61. 62. 6.5 units 63. 11.7 units 64. B 65. I 1-6

83. The Coordinate Plane 66. A 67. C 68. A 69. [2] a. (–10, 8), (–1, 5), (8, 2) b. Yes, R must be (–10, 8) so that RQ = 160. [1] part (a) correct or plausible explanation for part (b) GEOMETRY LESSON 1–6 70. 71. 72. 73. 74. 10 75. 10 76. 48 77. TAP , PAT 78. 150 1-6

84. The Coordinate Plane GEOMETRY LESSON 1-6 1. Find the distance between A and B to the nearest tenth. 2. Find BC to the nearest tenth. 3. Find the midpoint M of AC to the nearest tenth. 4. B is the midpoint of AD . Find the coordinates of endpoint D . 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? 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 A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6). 12.4 5.4 (–1, 1) (–3, –16) 500 mi 1-6

85. Perimeter, Circumference, and Area (For help, go to the Skills Handbook page 719 and Lesson 1-6.) Simplify each absolute value. 1. |4 – 8| 2. |10 – (–5)| 3. |–2 – 6| Find the distance between the points to the nearest tenth. 4. A (2, 3), B (5, 9) 5. K (–1, –3), L (0, 0) 6. W (4, –7), Z (10, –2) 7. C (–5, 2), D (–7, 6) 8. M (–1, –10), P (–12, –3) 9. Q (–8, –4), R (–3, –10) GEOMETRY LESSON 1-7 1-7

86. Perimeter, Circumference, and Area 4. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (5 – 2) 2 + (9 – 3) 2 d = 3 2 + 6 2 d = 9 + 36 = 45 To the nearest tenth, AB = 6.7. 6. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (10 – 4) 2 + ( – 2 –(– 7)) 2 d = 6 2 + 5 2 d = 36 + 25 = 61 To the nearest tenth, WZ = 7.8. 2. | 10 – (–5) | = | 10 + 5 | = | 15 | = 15 GEOMETRY LESSON 1-7 1. | 4 – 8 | = | –4 | = 4 Solutions 3. | –2 – 6 | = | –8 | = 8 5. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (0 – (–1)) 2 + (0 – (–3)) 2 d = 1 2 + 3 2 d = 1 + 9 = 10 To the nearest tenth, KL = 3.2. 7. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (– 7 – (– 5)) 2 + (6 – 2) 2 d = (–2) 2 + 5 2 d = 4 + 16 = 20 To the nearest tenth, CD = 4.5. 1-7

87. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 Solutions (continued) 1-7 8. 9. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (–12 – (–1)) 2 + (–3 – (–10)) 2 d = (–11) 2 + 7 2 d = 121 + 49 = 170 To the nearest tenth, MP = 13.0. d = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 d = (–3 – (–8)) 2 + (–10 – (–4)) 2 d = 5 2 + (–6) 2 d = 25 + 36 = 61 To the nearest tenth, QR = 7.8.

88. Perimeter, Circumference, and Area The perimeter is 56 ft. P = 4 s Formula for perimeter of a square P = 4( 14 ) = 56 Substitute 14 for s . GEOMETRY LESSON 1-7 1-7 Margaret’s garden is a square 12 ft on each side. Margaret wants a path 1 ft wide around the entire garden. What will the outside perimeter of the path be? Because the path is 1 ft wide, increase each side of the garden by 1 ft. s = 1 + 12 + 1 = 14

89. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 1-7 C = 2 ( 6.5 ) Substitute 6.5 for r . The circumference of G is 13 , or about 40.8 cm. . C = 13 Exact answer. C = 13 40.840704 Use a calculator. C = 2 r Formula for circumference of a circle. G has a radius of 6.5 cm. Find the circumference of G in terms of . Then find the circumference to the nearest tenth. . .

90. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 BC = |11 – 9| = |2| = 2 Ruler Postulate DA = |2 – 0| = |2| = 2 Ruler Postulate 1-7 Quadrilateral ABCD has vertices A (0, 0), B (9, 12), C (11, 12), and D (2, 0). Find the perimeter. Draw and label ABCD on a coordinate plane. Find the length of each side. Add the lengths to find the perimeter. AB = (9 – 0) 2 + (12 – 0) 2 = 9 2 + 12 2 Use the Distance Formula. = 81 + 144 = 255 = 15 CD = (2 – 11) 2 + (0 – 12) 2 = (–9) 2 + (–12) 2 Use the Distance Formula. = 81 + 144 = 255 = 15

91. Perimeter, Circumference, and Area = 15 + 2 + 15 + 2 = 34 The perimeter of quadrilateral ABCD is 34 units. GEOMETRY LESSON 1-7 1-7 (continued) Perimeter = AB + BC + CD + DA

92. Perimeter, Circumference, and Area Write both dimensions using the same unit of measurement. Find the area of the rectangle using the formula A = bh . 36 in. = 3 ft Change inches to feet using 12 in. = 1 ft. A = 12 You need 12 ft 2 of fabric. GEOMETRY LESSON 1-7 1-7 A = bh Formula for area of a rectangle. A = (4)(3) Substitute 4 for b and 3 for h . To make a project, you need a rectangular piece of fabric 36 in. wide and 4 ft long. How many square feet of fabric do you need?

93. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 1-7 A = r 2 Formula for area of a circle A = ( 1.5 ) 2 Substitute 1.5 for r . A = 2.25 In B , r = 1.5 yd. . The area of B is 2.25 yd 2 . . Find the area of B in terms of . .

94. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 Find the area of the figure below. 1-7 Draw a horizontal line to separate the figure into three nonoverlapping figures: a rectangle and two squares.

95. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 A R = b h Formula for area of a rectangle A R = ( 15 )( 5 ) Substitute 15 for b and 5 for h . A R = 75 A S = s 2 Formula for area of a square A S = ( 5 ) 2 Substitute 5 for s . A S = 25 A = 75 + 25 + 25 Add the areas. A = 125 The area of the figure is 125 ft 2 . 1-7 Find each area. Then add the areas. (continued)

96. Perimeter, Circumference, and Area 1. 22 in. 2. 36 cm 3. 56 in. 4. 78 cm 5. 120 m 6. 48 in. 7. 38 ft 8. 15 cm 9. 10 ft 10. 3.7 in. 11. m 12. 56.5 in. 13. 22.9 m 14. 1.6 yd 15. 351.9 cm GEOMETRY LESSON 1–7 16. 14.6 units 17. 25.1 units pages 55–58 Practice and Problem Solving 1 2 1-7

97. Perimeter, Circumference, and Area 29. in. 2 30. 0.25 m 2 31. 9.9225 ft 2 32. 0.01 m 2 33. 153.9 ft 2 34. 54.1 m 2 35. 452.4 cm 2 36. 452.4 in. 2 37. 310 m 2 38. 19 yd 2 20. 1 ft 2 or 192 in. 2 21. 4320 in. 2 or 3 yd 2 22. 1 ft 2 of 162 in. 2 23. 8000 cm 2 or 0.8 m 2 24. 5.7 m 2 or 57,000 cm 2 25. 120,000 cm 2 or 12 m 2 26. 6000 ft 2 or 666 yd 2 27. 400 m 2 28. 64 ft 2 GEOMETRY LESSON 1–7 18. 16 units 19. 38 units 1 3 1 8 2 3 9 64 1-7

98. Perimeter, Circumference, and Area GEOMETRY LESSON 1–7 39. 24 cm 2 40. 80 in. 2 41. a. 144 in. 2 b. 1 ft 2 c. 144; a square whose sides are 12 in. long and a square whose sides are 1 ft long are the same size. 42. a. 30 squares b. 16; 9; 4; 1 c. They are =. Post 1-10 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. 49. 16 cm 50. 96 cm 2 51. 288 cm 43. 3289 m 2 44–47. Answers may vary. Check students’ work. Samples are given. 44. 38 in.; 90 in. 2 45. 39 in.; 93.5 in. 2 46. 12 ft; 8 ft 2 47. 8 ft; 3.75 ft 2 1-7

99. Perimeter, Circumference, and Area GEOMETRY LESSON 1–7 52. a. Yes; every square is a rectangle. b. Answers may vary. Sample: No, not all rectangles are squares. c. A = ( ) or A = 53. 512 tiles 56. 38 units 57. 54 units 2 58. 1,620,000 m 2 59. 30 m 60. (4x – 2) units 61. Area; the wall is a surface. 62. Perimeter; weatherstripping must fit the edges of the door. 54. perimeter = 10 units area = 4 units 2 55. perimeter = 16 units area = 15 units 2 P 4 P 2 16 2 1-7

100. Perimeter, Circumference, and Area 63. Perimeter; the fence must fit the perimeter of the garden. 64. Area; the floor is a surface. 65. 6.25 units 2 GEOMETRY LESSON 1–7 b. c. 25 ft by 50 ft 66. a. base height area 1 98 98 2 96 192 3 94 282 : : 24 52 1248 25 50 1250 26 48 1248 : : 47 6 282 48 4 192 49 2 98 1-7

101. Perimeter, Circumference, and Area GEOMETRY LESSON 1–7 67. a. 9 b. 9 c. 9 d. 9 68. units 2 69. units 2 70. (9 m 2 – 24 mn + 16 n 2 ) units 2 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 83. 9.2 units; (1, 6.5) 84. 6.7 units; (–2.5, –2) 85. 90 86. WI RI 87. 62 units 88. 18 units 89. 6 units 90. 33 units 74. 2336 75. 540 76. 216 77. 810 78. (15, 13) 79. 8.5 units; (5.5, 5) 80. 5.8 units; (1.5, 5.5) 81. 13.9 units; (3, 5.5) 82. 6.4 units; (–2, 3.5) 3 a 20 25 a 2 4 1-7

102. Perimeter, Circumference, and Area GEOMETRY LESSON 1-7 256 in. 2 296 in. 30 ft 2 42 units 1-7 81 cm 2 A rectangle is 9 ft long and 40 in. wide. 1. Find the perimeter in inches. 2. Find the area in square feet. 3. The diameter of a circle is 18 cm. Find the area in terms of . 4. Find the perimeter of a triangle whose vertices are X (–6, 2), Y (8, 2), and Z (3, 14). 5. Find the area of the figure below. All angles are right angles.

103. Tools of Geometry GEOMETRY CHAPTER 1 1. Div. each preceding term by –2; , – 2. Add 2 to the preceding term; 10, 12 3. Rotate the U clockwise one-quarter turn. Alphabet is backwards; 8. B 9. a. 1 b. infinitely many c. 1 d. 1 10. 29,054.0 ft 2 11. never 12. sometimes 13. never 14. always 15. never 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. 5. A , B , C 6. Answers may vary. Sample: A , B , C , D 7. Answers may vary. Sample: A , B , D , E 1 2 1 4 TEST

104. Tools of Geometry 16. 10 17. a. (11, 19) b. MC = MD = 136 18. 19.1 units 19. 800 cm 2 or 0.08 m 2 20. 12.25 in. 2 21. 63.62 cm 2 22. 7 23. 9 31. 33 yd 2 1. D 2. G 3. B 4. H 5. B 6. I 7. B 8. H 9. 61 in. 10. 756 in. 2 11. 207 in. 12. 2 in. 24. Answers may vary. Sample: Some ways of naming an can help identify a side or vertex. 25. 26. Bisector 27. VW 28. 7 units 29. AY 30. E , AY 1 3 1 2 1 4 GEOMETRY CHAPTER 1 TEST