Elementary geometry for college students

630 Pages·2015·113.575 MB·English

by  Alexander, Daniel C.;Koeberlein, Geralyn M

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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
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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
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6E
Elementary
Geometry
for College Students
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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
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Elementary Geometry for College Students, © 2015, 2011,Cengage Learning
Sixth Edition
WCN: 02-200-203
Daniel C. Alexander
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Geralyn M. Koeberlein
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