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95698_FM.qxp 9/27/13 10:48 AM Page iv 95698_FM_Endsheet.qxp 9/13/13 1:50 PM Page 2 Formulas PLANE FIGURES: Kite: P (cid:2) 2a (cid:6) 2b P (cid:2) Perimeter; C (cid:2) Circumference; A (cid:2)Area ad1 b A (cid:2) 1 (cid:3) d (cid:3) d a d2 b 2 1 2 Triangle: P (cid:2) a (cid:6) b (cid:6) c c 1 Circle: a h A (cid:2) bh C (cid:2) 2pror C (cid:2) pd 2 A (cid:2) (cid:2)s(s (cid:4) a)(s (cid:4) b)(s (cid:4) c), r A (cid:2) pr2 b where s(cid:2)semiperimeter, so 1 s (cid:2) (a (cid:6) b (cid:6) c) 2 Regular Polygon (nsides): P (cid:2) n (cid:3) s Equilateral Triangle: 1 P (cid:2) 3s s A (cid:2) aP 2 s2 a A (cid:2) (cid:2)3 4 s MISCELLANEOUS FORMULAS: Right Triangle: Rectangle: P (cid:2) 2b (cid:6) 2h c2 (cid:2) a2 (cid:6) b2 A (cid:2) bhor A (cid:2) (cid:2)w c b A (cid:2) 1ab h 2 a b Polygons (nsides): Parallelogram: Sum (interior angles) (cid:2) (n (cid:4) 2) (cid:3) 180° P (cid:2) 2a (cid:6) 2b Sum (exterior angles) (cid:2) 360(cid:5) a h A (cid:2) bh Number (of diagonals) (cid:2) n(n (cid:4) 3) 2 b Regular Polygon (nsides): I (cid:2) Interior angle measure, E (cid:2) Exterior angle measure, and C (cid:2) Central angle measure Trapezoid: b1 P (cid:2) a (cid:6) b1 (cid:6) c (cid:6) b2 I (cid:2) (n (cid:4) 2)(cid:3)180° a h c A (cid:2) 21h(b1 (cid:6) b2) I E E (cid:2) 360° n C n 360° b2 C (cid:2) n Square: P (cid:2) 4s Sector: (cid:2) A (cid:2) s2 (cid:2) mAB A (cid:2)AB (cid:2) (cid:3)2pr 360° (cid:2) s B A (cid:2) mAB (cid:3)pr2 360° Rhombus: P (cid:2) 4s d1 s A (cid:2) 1 (cid:3)d (cid:3)d d2 2 1 2 s Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM_Endsheet.qxp 9/13/13 1:50 PM Page 3 SOLIDS (SPACE FIGURES): ANALYTIC GEOMETRY: L (cid:2) Lateral Area; T (or S) (cid:2)Total (Surface) Cartesian Plane Area; V (cid:2)Volume y Distance: d (cid:2) (cid:2)(x (cid:4) x)2 (cid:6) (y (cid:4) y)2 10 2 1 2 1 Parallelepiped (box)h: V T (cid:2)(cid:2) (cid:2)2w(cid:2)wh (cid:6) 2(cid:2)h (cid:6) 2wh (x1, y1) 8642 (x2, y2) MMid(cid:2)poi(cid:3)nxt1: (cid:6)2 x2, y1 (cid:6)2 y2(cid:4) x –10–8–6–4–2–2 2 4 6 8 10 y (cid:4) y w ––46 Slope: m (cid:2) x22 (cid:4) x11, x1 (cid:3) x2 –8 Parallel Lines: –10 (cid:2) (cid:5)(cid:2) 4m (cid:2) m Right Prism: 1 2 1 2 L (cid:2) hP Perpendicular Lines: T (cid:2) L (cid:6) 2B (cid:2)1(cid:2) (cid:2)2 4 m1(cid:3)m2 (cid:2) (cid:4)1 h V (cid:2) Bh Equations of a Line: Slope-Intercept: y (cid:2) mx (cid:6) b Point-Slope: y (cid:4) y (cid:2) m(x (cid:4) x) Regular Pyramid: General: Ax (cid:6) By 1(cid:2) C 1 1 L (cid:2) (cid:2)P 2 Cartesian Space h (cid:2)2 (cid:2) a2 (cid:6) h2 Distance: d (cid:2) (cid:2)(x (cid:4) x)2 (cid:6) (y (cid:4) y)2 (cid:6) (z (cid:4) z)2 2 1 2 1 2 1 a T (cid:2) L (cid:6) B (cid:3)x (cid:6) x y (cid:6) y z (cid:6) z (cid:4) 1 Midpoint: M (cid:2) 1 2, 1 2, 1 2 V (cid:2) Bh 2 2 2 3 Equations of a Line: Vector Form: (x, y, z) (cid:2) (x, y, z) (cid:6) n(a, b, c) 1 1 1 Right Circular Cylinder: Point Form: (x, y, z) (cid:2) (x (cid:6) na, y (cid:6) nb, z (cid:6) nc) 1 1 1 L (cid:2) 2prh T (cid:2) 2prh (cid:6) 2pr2 Equation of a Plane: h V (cid:2) pr2h Ax (cid:6) By (cid:6) Cz (cid:2) D r TRIGONOMETRY: Right Circular Cone: L (cid:2) pr(cid:2) Right Triangle: h (cid:2)2 (cid:2) r2 (cid:6) h2 sin u (cid:2) opposite (cid:2) a T (cid:2) pr(cid:2) (cid:6) pr2 hypotenuse c r V (cid:2) 1pr2h c a cos u (cid:2) adjacent (cid:2) b 3 (cid:10) hypotenuse c b opposite a Sphere: tan u (cid:2) (cid:2) adjacent b S (cid:2) 4pr2 r 4 sin2 u (cid:6) cos2 u (cid:2) 1 V (cid:2) pr3 3 Triangle: (cid:7) A (cid:2) 1bc sin a Miscellaneous: b a 2 Euler’s Equation: V (cid:6) F (cid:2) E (cid:6) 2 sin a sin b sin g (cid:8) (cid:9) (cid:2) (cid:2) c a b c c2 (cid:2) a2 (cid:6) b2 (cid:4) 2ab cos g or a2 (cid:6) b2 (cid:4)c2 cos g (cid:2) 2ab Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. 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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM_i-ii.indd 1 9/30/13 3:47 PM Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM_i-ii.indd 2 9/30/13 3:47 PM 95698_FM.qxp 9/27/13 10:48 AM Page iii 6E Elementary Geometry for College Students Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM.qxp 9/27/13 10:48 AM Page iv Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM.qxp 9/27/13 10:48 AM Page v 6E Elementary Geometry for College Students Daniel C. Alexander Parkland College, Professor Emeritus Geralyn M. Koeberlein Mahomet-Seymour High School, Mathematics Department Chair, Retired Australia • Brazil • Mexico • Singapore • United Kingdom • United States Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest. Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 95698_FM_i-ii.indd 2 9/30/13 3:47 PM 95698_FM.qxp 9/27/13 10:48 AM Page vi Elementary Geometry for College Students, © 2015, 2011,Cengage Learning Sixth Edition WCN: 02-200-203 Daniel C. Alexander ALL RIGHTS RESERVED. No part of this work covered by the copyright herein Geralyn M. 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