Sphere
i
i
in
Total area
TA = 4πr2
Volume
V = 43 πr3
Circumference
Volume
V = 13 Bh
Area
(Perimeter of circle)
Lateral area
LA =πrl
Total area
Volume
TA = Ph + 2B V = 13 Bh
= 2πr•h + 2πr2
Pyramid
r
Cone
Total area
TA = πrl + B
Lateral area
LA = 12 Pl
Length of
an ARC
= Circumference • degrees
= 2πr•(θ/360)
Total area
TA = 12 Pl + B
Area of
a SECTOR
= Area of circle • degrees
= πr2•(θ/360)
Triangle Congruency
e
a
s
ARIA
r
Area of
EQUILATERAL
TRIANGLE
Horizontal lines
s = side length
or x = number
Ex: x = 4, x = -1
Area of 2-D Shapes
Parallelogram A = bh
Triangle
A = 1/2 bh
Trapezoid
A = 1/2 (b1 + b2)•h
Circle
A = πr 2
Rhombus/Kite A = 1/2 d1•d2
Regular Polygon A = 1/2 aP
Radius in Shapes
Slope
Midpoint
Parallel Lines SAME SLOPE
Perpendicular Lines
OPPOSITE SIGN, RECIPROCAL
C = 2πr C = πd
A = πr
radius= 1/2 diameter
d
r
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3X
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r
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r = radius
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2
a
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or y = number
Ex: y = 4, y = -1
2
A = s √3
4
Vertical lines
slope is undefined
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Xi
x
Heron’s Formula
Area = √s(s - a)(s - b)(s - c)
s = semiperimeter = 1/2 perimeter
a, b, c = lengths of sides of Δ
a = apothem
Distance
kid
1st.tt
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Area of Δ
when length
of all 3 sides
are known
900
d
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Pythagorean Theorem
aZ b2
Z
c
c
a
Cos
Tan
0 opposite
sino H
hypotenuse r
e
O
a sin H
a adjacent
cost H
hypotenuse
pyroxene
a cos A
ti
f
0 opposite
tano A
adjacent
pyroxene
0
o tan A
f
Polygon Angle Measures
Sum of interior angles = 180(n - 2)
n = # of sides of polygon
Altitude on
Hypoteneuse
S OH
µµ
f
Dy
i
e
adjacent
Interior Degrees of Shapes
Sum of interior angles = 180(n - 2)
Triangle (3-sides)
Quadrilateral (4-sides)
Pentagon (5-sides)
Hexagon (6-sides)
180�
360�
540�
720�
P = perimeter A = area
V = volume
d1, d2 = diagonals
CAH
e
Dy
adjacent
n 2
n
Interior Angle Measure =180
Exterior Angle Measure =
360in
f
L
Y
i
o
a
e
Dy
adjacent
TO A
Geometric
Mean
h
x
y
Number of DIAGONALS in n-sided polygon
Number of diagonals =
Sum of Ext Angles = 360� ALWAYS
l = length
w = width
r = radius
a = apothem b = base
d = diameter
n
r
b
Sin
s
o
v
y = 0x + b, slope = 0
SSS Side Side Side
Examples
SAS Side Angle Side
on opposite
side
ASA Angle Side Angle
AA Angle Angle
HL Hypoteneuse Leg
CPCTC Corresponding Parts
Congruent Triangles are Congruent
2
v
E
r
a
a + b = 180 Therefore the two
angles are supplementary
r
Total area
Volume
TA = Ph + 2B
V = Bh
= (2l+2w)•h + 2lw = πr2•h
Volume
V = Bh
= lw•h
a
Lateral area
LA = Ph
= 2πr•h
Supplementary Angles ADD UP TO 180�
Cylinder
Lateral area
LA = Ph
= (2l + 2w)•h
a + b = 90 Therefore the two
angles are complementary
Conditionals: IF, THEN ••• Converse - SWITCH if/then ••• Inverse - NEGATE if/then ••• Contrapositive - SWITCH if/then, NEGATE
Prism/Cube
l = slant height
h = height
n(n - 3)
2
CuteCalculus.com
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Complementary Angles ADD UP TO 90�
P = perimeter of base
B = area of the base
GEOMETRY, Sheet 1
SOH
Sin = O/H
CAH
cos = A/H
Circles
150
300
150
750
450
20
a
XFL
7
b
a
a b
2
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r
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b
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Circles
F
90
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xyz
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SAS
Base
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Asina.es
va
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Segment Addition Postulate
4 22
A
BBisan
c
B
AB 1 BT_AT
anglebisector
Equation of a circle with center (h, k)
X h
h k
2
y k
2
center
Tutoring available @CuteCalculus
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A
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1314
1516
78
Alternate Interior Angles ARE EQUAL: 3 and 6, 4 and 5, 11 and 14, 12 and 13
Alternate Exterior Angles ARE EQUAL: 1/8, 2/7, 9/16, 10/15
5,6
E
l
A
A
ASA
a a
n
i
iz
34
Base
i
S S
1800
3600
a b
XR
S S
SSS
Same side Interior angles are SUPPLEMENTARY
Same side Exterior angles are SUPPLEMENTARY
b
B
l I
n
n
obtuse straight
Line
atbtotdte
30 60 90
X xf3 2X
f x S xg
S
x
Angles
I 90 T goo
right
acute
x
Triangle Congruency
Sector
9
aneradius
60
450
X X
x
2X
Xf3
45 45 90
tangent
v
diameter
2
X
inner
Em'e
r
tan = O/A
Special Right Triangles
150
x
TOA
Alternate INTERIOR are on
opposite sides of the transversal,
inside the parallel lines.
Alternate EXTERIOR are on
opposite sides of the transversal,
outside the parallel lines.
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iz
34
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Same Side INTERIOR are on
same side of the transversal,
inside the parallel lines.
Same Side EXTERIOR are on
same side of the transversal,
outside the parallel lines.
Same Side Interior Angles ADD TO
EQUAL 180: 3/5, 4/6, 11/13, 12/14
Same Side Exterior Angles ADD TO
EQUAL 180: 1/7, 2/8, 9/15, 10/16
iz
34
5,6
Corresponding angles
CORRESPOND to the exact
same position on a parallel line
intersection of the transversal.
For example, angles 1 and 5 are
both in the top left position at
both intersections.
Corresponding Angles
ARE EQUAL: 1/5, 2/6, 3/7, 4/8, 9/13,
10/14, 11/15, 12/16
iz
34
so
78
Vertical angles are ACROSS THE
INTERSECTION from each other
and are equal.
For example, angles 2 and 3 are
across the intersection and are
therefore equal.
Vertical Angles ARE EQUAL:
1/4, 2/3, 5/8, 6/7
Reference sheets available for Algebra 1 & 2, Precal and Calculus