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Formulas
Angles
Circles
Sum of the measures of the interior angles of a
triangle: 1808 (p. 218)
Angle and segments formed
by two chords:
1
Sum of the measures of the interior angles of a
convex n-gon: (n 2 2) p 1808 (p. 507)
Exterior angle of a triangle:
m∠ 1 5 m∠ A 1 m∠ B
C
C
D
m∠ 1 5 }
(m CD 1 m AB )
2
(p. 681) A
EA p EC 5 EB p ED
(p. 689)
E
(p. 219)
exterior
1 angle
Sum of the measures of the exterior angles of a
convex polygon: 3608 (p. 509)
C
Angle and segments formed
by a tangent and a secant:
E
C
C
A
2
1
m∠ 2 5 }
(m BC 2 m AB )
(p. 681)
EB2 5 EA p EC
(p. 691)
2
B
Right Triangles
A
Pythagorean Theorem:
c 2 5 a2 1 b2 (p. 433)
Angle and segments formed
by two tangents:
E
A
c
b
C
a
Trigonometric ratios:
BC
sin A 5 }
(p. 473)
AB
AC
cos A 5 }
(p. 473)
AB
BC
tan A 5 }
(p. 466)
AC
sin
458-458-908
triangle (p. 457)
308-608-908
triangle (p. 459)
C
C
1
m∠ 3 5 }
(m AQB 2 m AB )
(p. 681)
EA 5 EB
(p. 654)
2
B
3
P
B
21 BC
} 5 m∠ A (p. 483)
AB
21 AC
cos
Angle and segments formed
E
by two secants:
} 5 m∠ A (p. 483)
AB
21 BC
tan } 5 m∠ A (p. 483)
AC
C
C
4
B
1
m∠ 4 5 }
(m CD 2 m AB )
(p. 681)
EA p EC 5 EB p ED
(p. 690)
2
C
A
D
Coordinate Geometry
458
x 2
x
608
2x
x
Given: points A(x1, y1) and B(x2, y 2)
1
2
1
2
Midpoint of }
AB 5 }
,}
308
458
1
x 3
x
Ratio of
sides:
}
1: 1 : Ï2
(p. 451)
CD
AD
}
y 1y
2
2
2
(p. 16)
}}
C
AB 5 (x2 2 x1)2 1 (y2 2 y1)2
(p. 17)
‹]› rise y2 2 y1
Slope of AB 5 }
run 5 }
x 2x
(p. 171)
2
(p. 449)
CD AB
CB AB
AC
BD
} 5 } , } 5 }, } 5 }
AD CB
AD
DB AC
CD
x 1x
Ï
Ratio
of sides:
}
1: Ï 3 : 2
n ABC , n ACD , n CBD
BD
CD
1
Slope-intercept form of a linear equation with
slope m and y-intercept b: y 5 mx 1 b
(p. 180)
A
D
} 5 }, and CD 5 Ï AD p DB (pp. 359, 452)
B
Standard equation of a circle with center (h, k)
and radius r: (x 2 h)2 1 (y 2 k)2 5 r 2
(p. 699)
Taxicab distance AB 5 ⏐x2 2 x1⏐ 1 ⏐y2 2 y1⏐
(p. 198)
922
Student Resources
C
B
B
A
TABLES
1
Perimeter
Surface Area
P 5 perimeter, C 5 circumference,
s 5 side, l 5 length, w 5 width,
a, b, c 5 lengths of the sides of a triangle,
r 5 radius
B 5 area of a base, P 5 perimeter,
C 5 circumference, h 5 height, r 5 radius,
l 5 slant height
Polygon:
P 5 sum of side lengths
(p. 49)
Square:
P 5 4s
(p. 49)
Rectangle:
P 5 2l 1 2w
(p. 49)
Triangle:
P5a1b1c
(p. 49)
Regular n-gon: P 5 ns
Circle:
(pp. 49, 765)
C 5 2πr
Right prism:
S 5 2B 1 Ph
(p. 804)
Right cylinder:
S 5 2B 1 Ch
5 2πr 2 1 2πrh
(p. 805)
1
Regular pyramid: S 5 B 1 }
Pl
1
S5B1}
Cl
Right cone:
2
5 πr 2 1 πrl
(p. 49)
C
C 3608
mAB
Arc length of AB 5 }
p 2πr
(p. 747)
(p. 811)
2
(p. 812)
S 5 4πr 2
Sphere:
(p. 838)
Volume
Area
V 5 volume, B 5 area of a base,
h 5 height, r 5 radius, s 5 side length
Cube:
V 5 s3
(p. 819)
V 5 Bh
(p. 820)
Square:
A 5 s2
(pp. 49, 720)
Prism:
Rectangle:
A 5 lw
(pp. 49, 720)
Cylinder: V 5 Bh 5 πr 2h
(p. 820)
Triangle:
1
A5}
bh
2
(pp. 49, 721)
1
Pyramid: V 5 }
Bh
(p. 829)
Parallelogram:
A 5 bh
(p. 721)
Trapezoid:
1
A5}
h(b1 1 b2) (p. 730)
2
Rhombus:
1
A5}
dd
2 1 2
Kite:
A5}
dd
2 1 2
1
1
}
Ï3s2
Equilateral triangle: A 5 }
4
3
(p. 731)
Cone:
Sphere:
1
1 2
V5}
Bh 5 }
πr h
3
4 3
V5}
πr
3
(p. 829)
3
(p. 840)
Miscellaneous
}
(p. 731)
Geometric mean of a and b: Ïa p b
(pp. 726, 766)
Euler’s Theorem for Polyhedra, F 5 faces,
V 5 vertices, E 5 edges: F 1 V 5 E 1 2
(p. 795)
(p. 359)
Regular polygon:
1
A5}
aP
(p. 763)
Given: similar polygons or similar solids
with a scale factor of a : b
Circle:
A 5 πr 2
(pp. 49, 755)
Ratio of perimeters 5 a : b
Area of a sector:
2
C
mAB
A5}
p πr 2
360°
2
(p. 756)
TABLES
A 5 area, s 5 side, b 5 base, h 5 height,
l 5 length, w 5 width, d 5 diagonal,
a 5 apothem, P 5 perimeter, r 5 radius
Ratio of areas 5 a : b
2
3
Ratio of volumes 5 a : b
(p. 374)
(p. 737)
3
(p. 848)
Given a quadratic equation ax 2 1 bx 1 c 5 0,
the solutions are given by the formula:
}
6 Ïb2 2 4ac
x 5 2b
}}
2a
(pp. 641, 883)
Tables
923