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Formula (given):
Volume of a Pyramid
V = 1/3 BH
What does B represent?
Formula:
Area of a Trapezoid
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Centroid
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Midsegment of a triangle
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Point Slope Form of
Linear Equation
*can be used to write
equation of a line
Slope formula
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Slope-Intercept Form
of linear equation
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Quadrilateral Family Tree
Midsegment of a Trapezoid
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Standard Form
Of Linear Equation
Area of the base.
B = triangle ½ bh
B = Rectangle lw
A = ½ h (b1 + b2)
Where the medians of a triangle intersect.
Each median is divided into a 2:1 ratio.
The segment closest to vertex is twice as long!
𝑚=
y - y = m(x - x )
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y 1 = y-coordinate x 1 = x-coordinate
m = slope
Rise
Run
𝑦2 −𝑦1
𝑥2 −𝑥1
Δy
Δx
y = mx + b
m = slope
b = y-intercept
Ax + By = C
where A,B, and C are real numbers
Substitute 0 in for x to find the y-intercept
Substitute 0 in for y to find the x-intercept
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Perpendicular Lines
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Parallel Lines
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Parallelogram Properties
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Rectangle Properties
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Square Properties
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Rhombus Properties
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Kite Properties
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Trapezoid Properties
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Isosceles Trapezoid
Quadrilaterals
Same Slopes
Negative Reciprocal Slopes
(Opposite Signs and Flipped)
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−3
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Example: and
At least 1 pair of parallel sides
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Constructing:
Perpendicular Bisector
Midpoint
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Constructing:
Angle Bisector
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Constructing:
Equilateral Triangle
60° angle
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Constructing:
Parallel Lines
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Constructing:
Perpendicular from a Point on the
line
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Constructing:
Perpendicular from a point NOT
on the line
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Reflection in x-axis
(x, y)
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Reflection in line y = x
(x, y)
Reflection in y-axis
(x, y)
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Reflection in line y = -x
(x, y)
(- x, y)
(x, - y)
(-y, -x)
(y, x)
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Point reflection through the Origin
(same as Rotation 180° CC)
(x, y)
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R90
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Isometry
(same as RIGID MOTION)
Preserves…
R270
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Opposite isometry
What transformations are rigid
motions (isometries)?
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Direct Isometry
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Composition of Transformations
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Orthocenter
Incenter
(-x, -y)
(-y, x)
(y, -x)
orientation is not preserved - the
order of the lettering is reversed
Line Reflections
Reflections, rotations, translations,
and glide reflections
are all examples of rigid motions.
(NOT DILATIONS)
orientation is preserved - the order of
the lettering in the figure
and the image are the same
Rotations, translations, POINT
reflections
Intersection of Angle Bisectorss
Intersection of Altitudes
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Circumcenter
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Isosceles Triangle
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Special Right Triangle
30°-60°-90°
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Special Right Triangle
45°-45°-90°
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How do you determine the longest
side of a triangle?
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Triangle Exterior Angle Theorem
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Altitude to Hypotenuse
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Distance Formula
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Slope Formula
Midpoint Formula
Intersection of Perpendicular Bisectors
45°-45°-90°
x
x
30°-60°-90°
x x√3 2x
Hidden in Equilateral
Triangle with altitude.
x√ 2
Hidden in Square
w/diagonal
If side opposite 90° is a whole #, ÷ √2 then rationalize to get
side opposite 45°.
Exterior angle = The sum of non-adjacent interior angles
If side opposite 60° is a whole #, ÷ √3 then rationalize to get
side opposite 30°.
Opposite the largest angle
𝑃𝐵
𝐿
𝐿
=𝐻
𝑃
𝐴
=𝑃
𝐴
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Cofunctions
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Sine
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Cosine
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Tangent
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Pythagorean Theorem
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When do you use Trig?
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When do you use the Pythagorean
Theorem?
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How to determine possible length
of 3rd side of a triangle.
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Area of a Regular Polygon
Apothem
Sin < =
𝑂𝑝𝑝
𝐻𝑦𝑝
If trying to find angle use sin-1
tan < =
𝑜𝑝𝑝
cos < =
𝑎𝑑𝑗
If trying to find angle use tan-1
Use when angle is involved in RIGHT triangle
𝑺
Sine and Cosine
They are = when angles are complementary.
 Sin (10°) = cos (80°)
 Find value of x: sin (x) = cos (x + 5)
Add angles and set to 90.
𝑶 𝑨 𝑶
𝑪 𝑻
𝑯 𝑯 𝑨
Given side, angle…Find other side
Given 2 sides…find angle
Given 2 sides of a triangle
Subtract them
Add them
3rd side must be between those lengths
Ex. 5 and 7
3rd side must be between 2 and 12 (not 2 or 12)
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Area of reg poly= 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 ∙ 𝑎𝑝𝑜𝑡ℎ𝑒𝑚
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𝑎𝑑𝑗
𝐻𝑦𝑝
If trying to find angle use cos-1
Triples:
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
Use when only sides of a right
triangle are involved.
Know 2 sides of a right triangle
Asked to find the third side
Segment drawn from the center of a regular polygon
to the midpoint of a side (will also be ⊥)
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2 tangents to a circle
(Segment/Angle Relationship)
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2 chords in a circle
(Segment/Angle Relationship)
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2 secants to a circle
(Segment relationship)
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Angle formed Outside the Circle
(angle relationship)
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Tangent /Secant
(Segment Relationship)
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Equation of a circle
(center at the origin)
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Central Angle
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Equation of a Circle
(center shifted)
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Inscribed Angles
Watch –Out
Secant/Tangent
Segments
Angles


tan = tan
minor arc is supplementary
to angle formed by 2 tangents
P•P=P•P
A•B=C•D
w • e = t2
(b+c) b = a2
we=we
(a+b)•b = (c+d)•d
Measure of angle = Measure of arc

opp signs of center!
o ½ arc
o Subtract from 180
Measure of angle = ½ arc
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Which point of concurrency
locates the point equidistant
from all 3 vertices
of a triangle?
Points of Concurrency
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Area of a KITE/Rhombus/Square
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Length of an Arc
(degrees)
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Area of a Sector of a Circle
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Length of an Arc
(Radians)
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Similar Triangles
4 proportions GOOD
1 proportion NOT GOOD!
Converting between
degrees and radians
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Similar Triangle Proofs
(last 3 steps)
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Inscribed Angle
that intercepts the diameter
All Of My Children Are Bringing In Peanut Butter Cookies
Perpendicuar Bisectors- Circumcenter
Altitudes-Orthocenter
Medians- Centroid
Angle Bisectors- Incenter
Perpendicuar Bisectors- Circumcenter
A = ½ d1 •d2
Portion of the Circumference
L=
𝑛°
360
∙ 𝜋𝑑
S = 𝜃𝑟
Portion of the Area
L=
𝜃 𝑖𝑠 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑖𝑛 𝑅𝐴𝐷𝐼𝐴𝑁𝑆
GOOD




𝐴𝐷
=
𝐷𝐵
𝐴𝐷
𝐴𝐵
𝐷𝐵
𝐴𝐵
𝐴𝐷
𝐷𝐸
𝑛°
360
∙ 𝜋𝑟 2
NOT GOOD
𝐴𝐸
𝐸𝐶
𝐴𝐸
PIECE/PIECE
𝐴𝐷
𝐷𝐸
=
𝐷𝐵
𝐵𝐶
= 𝐴𝐶 PIECE/WHOLE
𝐸𝐶
= 𝐴𝐶 PIECE/WHOLE
=
𝐴𝐵
𝐵𝐶
WHOLE/WHOLE
Is a right angle!
Δ ~
Δ
=
( )( ) = ( )( )
AA
CSSTP
In a proportion, the
product of the
means = product of
the extremes.
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Cavalieri’s Principle
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Dilation
with Respect to the ORIGIN
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Segment Perpendicular
to a chord
Dilation with Respect to a POINT
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What does CSSTP
stand for?
What does CPCTC
stand for?
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What congruence criteria can be
used to prove 2 triangles are
congruent?
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Dilating a LINE
With respect to origin
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How do you prove 2 triangles are
Similar?
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Angle of
Elevation/Depression
Multiply pre-image points by scale
factor.
DK, O (x, y) = (kx, ky)
Bisects the chord
Corresponding Sides of Similar
Triangles are Proportional
Two solids will have equal volumes if their bases have
equal area and their altitudes (heights) are equal
Point of dilation, image and pre-image must
be collinear.
Corresponding Parts of Congruent
Triangles are Congruent
AA
Multiply y-intercept by
scale factor
SLOPE STAYS SAME!
Ex. D2,O y= 2x – 4
Becomes y = 2x – 8
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Why are all circles similar?
Altitude of an isosceles triangle is
also …
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Writing an equation of
perpendicular bisector
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How to construct a
SQUARE INSCRIBED
IN A CIRCLE
Partitioning a
Directed Segment
How to construct a
Equilateral Triangle / Hexagon
INSCRIBED IN A CIRCLE
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Rotational Symmetry
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Point Symmetry
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Coordinate Geometry Proofs
Completing the Square for a
CIRCLE
x2 + y2 + cx + dy = e
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Bisects Vertex Angle
Bisects the BASE
Composition of a Translation
and Dilation.
1st Find Midpoint
2nd Find Slope
3rd find Negative Reciprocal of slope.
Then use y – y1 = m(x – x1) with your midpoint and
NR slope
Divide the slope (rise and run)
Example 2:3 ratio, divide rise and run by 5.
Then count new slope to create partition
Looks the SAME after a rotation
of 180 (turn upside down)
Parallelogram: 4 SLOPES (Opp. Sides ||)
Rectangle: 4 SLOPES (Opp. Sides ||, 1 pair
consecutive sides ⊥)
Rhombus: 6 SLOPES (Opp. Sides ||, diagonals ⊥)
Square: 6 SLOPES (Opp. Sides ||, 1 pair consecutive
sides ⊥, diagonals ⊥)
Trapezoid: 2 SLOPES (1 pair of || sides)
Isosceles Trapezoid: 2 SLOPES, 2 DIST (1 pair of ||
sides, non || sides congruent)
Measure radius, mark off radius
(creating 60° central angle)
Looks the SAME after a rotation
Maps onto itself
𝑏 2
( ) , 𝑎𝑑𝑑 𝑡𝑜 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠
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