Download Geometry Study Sheet - Pender County Schools

Geometry Study Sheet
Unit 01 Basic Geometry
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Distance Formula
d
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x  x  y  y 
2
2
xx yy
,
Midpoint 
2 
 2
3D Coordinates
 x, y, z   F / B, R / L, T / B 
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Inverse – not
Contrapositive – switch & not
Pythagorean Theorem
a2  b2  c 2
F-prop angles are =
Z-prop angles are =
C-prop angles =180
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Switch:
Converse – switch
Unit 02 Transformations
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Translation, slide, is matrix
x  x x x 
addition    

y  y y y 
X-direction left/right, -, +
Y-direction down/up, -, +
Find rule first, then stay/switch,
then signs
When multiplying matrices
stay/switch first, then signs
new x   1 0 
Stay:
0 1  new y


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0 1  new x
new y   1 0 
Rules
o y  x :  y, x 
o y   x :  y ,  x 
o Use paper for
rest
 x-axis
 y-axis
 90, 180,
270
 cw/ccw
Unit 03 Basic Triangles
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180 in a triangle
2 inside angles = outside angle
Sides opposite = angles are =
Bigger sides opposite bigger
angles, smaller opp. Smaller
2 smallest sides have to be
bigger than the biggest
Midsegment 2  middle   base
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Angle
Bisector
Median
Perp
Bisector
Altitude
y
x
Unit 04 Right Triangles
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SohCahToa
Angle of elevation/depression always in the bottom of the triangle
Calculator in degree mode
If asked for angle use 2nd sin/cos/tan
a
gm
Geometric mean

gm
b
Case 1
Case 2
gm
gm
b
a
a
b
Leg, part, whole
Alt, part, part
Unit 05 Proof in Triangles
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Congruence Statements
o SSS
o ASA
o SAS
o AAS
o HL (right triangles ONLY)
CPCTC (corresponding parts of
congruent triangles congruent)
Similar triangles have same
shape, but are different sizes
Unit 06 Midterm
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Review Previous units
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Setup proportions
A A

B B
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Parallel lines cut transversals
proportiona
lly
Angle
bisector
cuts sides
proportionally
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Unit 07 Quadrilaterals
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Parallelograms
o Opp. Angles =
o Opp. Sides =
o Diagonals each other
o Consecutive angles = 180
Rhombuses
o Same properties as
parallelograms
o Diagonals bisect the
angles
o Diagonals are
perpendicular
Rectangles
o Same properties as
parallelograms
o Diagonals are =
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Squares
o Same properties as
parallelograms
o Same properties as
rhombuses
o Same properties as
rectangles
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Trapezoids\Isosceles Trapezoids
o Midsegment in all
trapezoids 2  middle   B  b
o Diagonals = in Iso. trap
o Base angles = in iso. trap
b
M idse gment
Unit 08 Circles
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C  d
Arc length  %C
A  r 2
Area of Sector %A
See the end of this sheet for concept maps
B
Unit 09 Area & Polygons
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Triangle
1
o A  bh
2
Parallelogram
o A  bh
Rhombus/Kite
1
o A  d1d2
2
Trapezoid
1
o A  B  b  h
2
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Circle
o A  r 2
o Sector %A
Polygons
o Area break up into
triangles
o Interior Angles
S  180n  360
o Exterior Angles always
360
Unit 10 Solids
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Prism/Cylinder Formulas
o LA  ph
o TA  2B  LA
o V  Bh
Pyramid/Cone Formulas (Will be
given)
1
o LA  pl
2
o TA  B  L
1
o V  Bh
3
Sphere Formulas
o TA  4 r 2
4
o V  r3
3
Similar Solids
o Scale a : b
o Surface Area Ratio a 2 : b 2
o Volume Ratio a3 : b3
Regular Polyhedrons
o Tetrahedron (4 Equilateral
Triangles)
o Hexahedron (6 Squares)
o Octahedron (8 Equilateral
Triangles)
o Dodecahedron (12
Regular Pentagons)
o Icosahedron (20
Equilateral Triangles)
Measure of central
x
Measure of inscribed
x
angle = intercepted arc
2x
x
angle = 1/2 intercepted arc
1
y
< formed by 2 tangents
Angle inscribed in a
m < 1 = 1/2 ( x - y )
x
semicircle is right
OR m < 1 + y = 180
1
ANGLES
IN
CIRCLES
y
180º
x
b
x
a + b = 180; x + y = 180
a
< formed by 2 secants
Inscribed quadrilateral
y
m < 1 = 1/2 ( x - y )
y
1
x
< formed by 2 chords
m < 1 = 1/2 ( x + y )
x
2x
< formed by chord and tangent
= 1/2 intercepted arc
Congruent chords cut
Diameter perpendicular
off congruent arcs
to chord bisects chord & arc
2 tangents from same
Tangent line is
point are congruent
perpendicular to radius
SEGMENTS
IN
CIRCLES
a
b
c
2 congruent chords
d
equidistant from center
2 secants
a (a + b) = c ( c + d)
b
d
a
b
c
a
2 chords
Tangent and secant
c
a•b=c• d
a ( a + b) = c^2