Honors Geometry Solutions Manual

1 Solutions Manual This booklet is provided in glencoe Geometry Answer Key Maker (0-07-860264-5). Also provided are Solutions for problems in the Prerequisite Skills, Extra Practice, and Mixed Problem Solving sections. Copyright by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge;. and be used solely in conjunction with glencoe Geometry . Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: glencoe /McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027. ISBN: 0-07-860204-1 Geometry Solutions Manual 1 2 3 4 5 6 7 8 9 10 009 12 11 10 09 08 07 06 05 04 03. CONTENTS. Chapter 1 Points, Lines, Planes, and Angles.. 1. Chapter 2 Reasoning and Proof.

2 24. Chapter 3 Parallel and Perpendicular Lines.. 54. Chapter 4 Congruent Triangles .. 85. Chapter 5 Relationships in Triangles ..120. Chapter 6 Proportions and Similarity ..151. Chapter 7 Right Triangles and Trigonometry.. 189. Chapter 8 Quadrilaterals.. 238. Chapter 9 Transformations.. 289. Chapter 10 Circles .. 345. Chapter 11 Areas of Polygons and Circles .. 383. Chapter 12 Surface Area .. 411. Chapter 13 Volume ..447. Prerequisite Skills 477. Extra Practice 502. Mixed Problem Solving and Proof 567. Chapter 1 Points, Lines, Planes, and Angles Page 5 Getting Started 2. See students' work; sample answer: Two lines 1 4. intersect at a point. y 3. Micha; the points must be noncollinear to D( 1, 2) determine a plane. 4. Sample answers: line p; plane R. B(4, 0) 5. Sample answer: y O x A(3, 2). C( 4, 4) W. x O. 5. 3. 3 6 3 X. 4 8 8 8 Z. 9 1 . 8 18.. 5 . Y. 1 37 4 . 1. 16 5 8 16 8. 6. 2 . 37 82 6. 16 16. r P. 11 9 7 . 16 7 16 s 9 . 7. 7 9.

3 14 Q. 8 16 16 16. 5 7. There are six planes: plane ABC, plane AGE, 16. plane CDE, plane BCD, plane FAB, and plane 8. 11 1 7 23 15 . 2 9 16 2 16. 1. DEF. 18 4 15 1. 16 16. 8. A, K, B or B, J, C. 33 9. No; A, C, and J lie in plane ABC, but D does not. 1 . 16 2 16.. 10. line 11. point 12. plane 9. 2 17 15. 10. 23 ( 14) 23 14. 37 Pages 9 11 Practice and Apply 11. [ 7 ( 2)]2 ( 7 2)2 13. n 14. F. ( 5)2 25 15. R 16. W. 12. 92 132 81 169 . 17. Sample answer: PR. 250. 13. P 4s 18. Yes, it intersects both m and n when all three 4(5) 20 lines are extended. The perimeter is 20 in. 19. (D, 9) 20. Charlotte 14. P 2 2w 21. B.. 2(6) 2 2 1.. 2. 12 5 17 W. The perimeter is 17 ft. Q. 15. P 2 2w A. 2( ) 2( ). 15 22. The perimeter is m. R. W. T. 23. Sample answer: 1-1 Points, Lines, and Planes y Page 8 Geometry Activity R S. 1. no 2. no Z.. 3. On CD; see students' work. O x 4. See students' work. Q. Page 9 Check for Understanding 1. point, line, plane 1 Chapter 1.

4 24. Sample answer: 36. Sample answer: points E, A, and B are coplanar, y but points E, A, B, and C are not. 37.. AC 38. point C R 39. lines 40. plane 41. plane P. D 42. two planes intersecting in a line 43. point 44. intersecting lines S O x 45. point 46. line 47. 25. a b c 48. 26. a F b V. c 27. s 49. See students' work. C r 50. Sample answer: the image is rotated so that the D front or back plane is not angled. M 51. Sample answer: 28. s A. B C. 52. See picture. 53. vertical 54. Sample answer: the paths flown by airplanes flying in formation 29. points that seem collinear; sample answer: 55. Sample answer: Chairs wobble because all four (0, 2), (1, 3), (2, 4), (3, 5). legs do not touch the floor at the same time. y Answers should include the following. The ends of the legs represent points. If all points lie in the same plane, the chair will not wobble. O x Because it only takes three points to determine a plane, a chair with three legs will never wobble.

5 56. C; Three lines intersect in a maximum of three points. The fourth line can cross the other three lines only one time each, adding three points to the figure. For example, 30. There are five planes: plane ABC, plane BCE, plane ABE, plane ADE, and plane CDE. 31. 1; There is exactly one plane through any three noncollinear points. 32. E, F, C. 33. Because A and B determine a line, add point G. anywhere on AB . 34. E, F 35. A, B, C, D or E, F, C, B. Chapter 1 2. 57. B; 2 x 2 x 2 x 2 2 x 2 1-2 Linear Measure and Precision x x x x x x 2x 0 Page 16 Check for Understanding Thus, x must be 0. 1. Align the 0 point on the ruler with the leftmost 58. y endpoint of the segment. Align the edge of the ruler along the segment. Note where the rightmost endpoint falls on the scale and read the closest eighth of an inch measurement. 2. Sample answers: rectangle, square, equilateral triangle 3. Each inch on the ruler is divided into eighths. O x Point Q is closer to the 1 6.

6 8 -inch mark. Thus, P Q is about 1 6. or 1 3 inches long. 8 4. a line 4. The long marks on the ruler are centimeters, and 59. y the shorter marks are millimeters. There are 10 millimeters for each centimeter. Thus, the bee is 13 millimeters or centimeters long. O x 5. The measurement is precise to within meter. So, a measurement of 14 meters could be to meters. 1. 6. The measuring tool is divided into 4 -inch increments. Thus, the measurement is precise to within 1. 1 1. 2 4 or 8 inch. Therefore, the part of the coordinate plane above the line measurement could be between 3 1 1 . 4 8 38. 1 . y 2x 1 inches and 3 1 1 3 . 4 8 3 8 inches.. 60. 1. 4 1 3 . 2 8 , so 2 in. 8 in. 7. EG EF FG. 4 . 61. 1 4 1 EG 4 16 , so 16 in. 4 in. EG 8 . 62. 4 4 6 . 5 10 , so 5 in. 10 in. G. So, E is centimeters long. 63. 10 mm 1 cm 8. XY YZ XZ. 64. cm 25 mm, so cm 28 mm XY 1 5 . 8 3. 65. cm mm, so cm 25 mm XY 1 5 5 5 . 8 1 8 3 1 8.. 3. XY 1 8 . 3. Y. So, X is 1 8 inches long.

7 Page 12 Reading Mathematics 9. 1. Points P, Q, and R lie on . Point T is not collinear 5x 3x with P, Q, and R. 15. 2. Planes F, G, and H intersect at line j. N L M. 3. The intersection of planes W, X, Y, and Z is NL 5x 15. point P. 5 x 15.. 4. 5 5. A x 3. B LM 3x C LM 3(3). LM 9. 10. 30. 6x 5 2x 3. N L M. NM NL LM. 30 6x 5 2x 3. 30 8x 2. 30 2 8x 2 2. 32 8x 3 . 2 8 . x 8 8. 3 Chapter 1. 4 x XZ 5.. 4. LM 2x 3. So, X is 5. Z 1 . 4 or 1 4 inches long. LM 2(4) 3 8 3. LM 11 24. PR PQ QR. C. 11. B C D because they both have length 5 . 2 1. 4 16 QR. 10 inches. 9 5. 1 6 . 5. 1 6 QR . 5 . 4 16. E. B E D because they both have length 8 inches. 36 5 . A. B D A because they both have length 16 16 QR.. inches. 31.. 16 QR. 31 15. So, Q R is . 16 or 1 16 inches long. Pages 17 19 Practice and Apply 25. RT RS ST. 12. Each inch on the ruler is divided into sixteenths. ST. Point B is closer to the 1 5 . B. -inch mark. Thus, A ST 16 ST. 5. is about 1 inches long.

8 16 T. So, S is centimeters long. 13. The long marks on the ruler are centimeters, and 26. WY WX XY. the shorter marks are millimeters. Point D is WX WX X. W is congruent to X. Y.. closer to the 45-millimeter mark. Thus, C D. is 2WX. about 45 millimeters or centimeters long. 2W X. 2 2. 14. The long marks on the ruler are centimeters, and . the shorter marks are millimeters. The right end WX. of the key is closer to the 33-millimeter mark. X. So, W is centimeters long. Thus, the key is about 33 millimeters or 27. AD AB BC CD. centimeters long. 3 3. 4 BC BC BC A. B is congruent to B. C.. 15. Each inch on the ruler is divided into sixteenths. D. and C is congruent to B C . The right tip of the paperclip is closer to the 3 3.. 4 4 4 3BC. 1 -inch mark. Thus, the paperclip is about 1 . 16. 1. or 1 4 inches long. 16.. 1 . 1 . 5 1 . 3 4 3 (3BC). 16. The measurement is precise to within 1 . 2 inch. So, 15.. 12 BC. a measurement of 80 inches could be 79 1 1.

9 2 to 80 2 C is 1 3 1. So, B 1 2 or 1 4 inches long. inches. 28. 7a 12a 17. The measurement is precise to within millimeter. So, a measurement of 22 millimeters 28. could be to millimeters. R S T. 18. The measuring tool is divided into 1 RS 7a 28. 2 -inch 7a 28. increments. Thus, the measurement is precise to . 7 7. within 1 . 1 1 . 2 2 or 4 inch. Therefore, the a 4. measurement could be between 16 1 1 1 . 2 4 16 4. ST 12a 1 1 3. inches and 16 2 4 16 4 inches. ST 12(4). 19. The measurement is precise to within ST 48. centimeter. So, a measurement of 308 centimeters 29. could be between and centimeters. 34. 20. The measurement is precise to within meter 12 2x or 5 millimeters. So, a measurement of meters 3750 millimeters could be between 3745. and 3755 millimeters. R S T. RT RS ST. 21. The measuring tool is divided into 1.. 4 -foot 34 12 2x increments. Thus, the measurement is precise to 34 12 12 2x 12. within 1 . 1 1 . 2 4 or 8 foot. Therefore, the 22 2x measurement could be between 2 2 2.

10 X 2 2.. 3 1. 1 1 1 1 3 . 4 8 3 8 feet and 3 4 8 3 8 feet. 11 x 22. AC AB BC ST 2x AC ST 2(11). C. So, A is millimeters long. ST 22. 23. XZ XY YZ. XZ 1. 3 2 3 . 2 4 4 4. Chapter 1 4. 30. 25 34. yes; AB CD 3 cm 35. no; EF 6 ft and FG 8 ft 2x 3x 36. no; NP in. and LM in. 37. yes; WX XY 6 m R S T 38. not from the information given RT RS ST 39. yes; TR 3(a b) 3c 3a 3b 3c 25 2x 3x SU 3a 3(b c) 3a 3b 3c 25 5x 40. The width of a music CD is 12 centimeters. 5. 2 5 x 5 5 41. F. C D G , A B. H I , C. E. E D. E F E G . 5 x 42. 144 cm3; 343 mL could be actually as much as ST 3x mL and 200 mL as little as mL;. ST 3(5) 144. ST 15. 43. The lengths of the bars are given in tenths of 31. 5x 10 millions, and million 100,000. So the graph is precise to within 50,000 visitors. 16 2x 44. 50,000 million, so a measurement of million could be million to million R S T visitors. RT RS ST 45. No; the number of visitors to Washington state 5x 10 16 2x parks could be as low as million or as high 5x 10 10 16 2x 10 as million.