Geometry Formulas

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10 Οκτ 2013 (πριν από 4 χρόνια και 29 μέρες)

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Geometry Formul
as


Rebecca Darko

Parrellogram


(Rectangle
, Rhombus
,Square
)




Area = b

* h

Square



Area = a*a =

a
2


Perimeter = 4a

Rectangle


Area = a * b

Perimeter = 2a + 2b

Rhombus



Perimeter = 4 * b

Trapezoid



Triangle



Perimeter = a * b *
c




Equilateral Triangle


Circle




Ellipse



Polygons

Sides

Name

n

N
-
gon

3

Triangle

4

Quadrilateral

5

Pentagon

6

Hexagon

7

Heptagon

8

Octagon

9

Nonagon

10

Decagon

12

Dodecagon

Polygons

Interior/Exterior Angles




Distance Formula


Midpoint


Slope


Lines


Point
-
Slope Form

y


y
1

= m * (x


x
1
)

Slope
-
Intercept Form

y = mx + b

Standard Form

ax + by = c


Cube




Rectangular Prism




Irregular Prism


Volume =b*h

Cylinder





Pyramid




Cone





Sphere




Ellipsoid



Geometry Formul
as


Rebecca Darko

Definitions

Complementary Angles
-

two angles
that add to 90°

Supplementary Angles
-

Two angles that add to 180°

Parallel Lines & Transversal


Theorems:

Corresponding (C): 1,8

Same
-
Side Exterior (S):1,7

Same
-
Side

Interior (S): 3.5

Alternate Interior (C): 3,6

Alternate Exterior (C): 1,8

Supplementary Angles (S): 1,2

Vertical Angles (C): 1,4

C = Complementary

S = Supplementary


Triangle
Theorems

Congruent Triangles

Side
-
Angle
-
Side (SAS)

Side
-
Side
-
Side

(SSS)

Angle
-
S
ide
-
Angle (ASA)

Angle
-
Angle
-
Side (AAS)

Hypotenuse
-
Leg (HL)

ASS or SSA not allowed.

CPCTC
if

triangles are congruent

Similar Triangles

Angle
-
Angle (AA)

Side
-
Side
-
Side (SSS)

Side
-
Angle
-
Side (SAS
)

Possible Triangles
-

SSA

If A is obtuse,



no triangle



one triangle

If A is acute,



no triangle


two triangles



one triangle



one triangle



Circle Angles

Definition of Arc
Measure



Chord/Tangent



Inscribed Angle Theorem



Two Chord Angle Theorem



Two Tangent Theorem



Two Secant Theorem



Secant/Tangent Theorem



Graphing Trigonometric
Functions


|a| = amplitude


c = horizontal shift

d = vertical shift


Polar Form

z = a + bi

a = rcos

b= rsin

z = rcos

+ isin



Parametric

x(t) = r cos(t) + j







y(t) = r sin(t) + k



Euler’s Equation


Theorems

Midpoint Theorem

Vertical Angles Theorem

Supplement Theorem

Right Angle Theorem

Complement Theorem

Perpendicular Transversal Thm

Angle Sum Theorem
-
Triangles

Exterior Angle Theorem

Base Angles Thm/Isosceles

Interior Angle Sum Theorem

Exterio
r Angle Sum Theorem

Triangle Inequality Theorem



Geometry Formul
as


Rebecca Darko

Definitions

Definition of Midpoint

Definition of Angle Bisector

Definition of Segment Bisector

Definition of Perpendicular Lines

Def.
-

Distance b/n a Point & Line

Definition of Similar Polygons

Definition
of Regular Polygon

Laws

Law of Detachment

If
and p, then q.

Law of Syllogism

If
&
then

Postulates

Segment Addition Postulate

Angle Addition Postulate

Trapezoids

-
Both pairs of base angles of isosceles
trapezoid are congruent.

-
Diagonals are congruent.

-
Median of trapezoid is parallel to the
bases; it’s measure is half the sum of
the measure of the bases.

Rhombus

-
Diagonals are perpendicular.

-
Each diagonal bisect
a pair of
opposite angles.

Parallelograms

-
Both pairs of opposite sides are
congruent.

-
Opposite angles are congruent.

-
Consecutive angles are
supplementary.

-
Diagonals bisect each other.

-
Both pairs of opposite angles are
congruent.

-
One pair of sides are

both parallel and
congruent.

Rectangle

-
Diagonals are congruent.

-
Opposite sides are congruent and
parallel.

-
Opposite angles are congruent.

-
Consecutive angles are
supplementary.

-
Diagonals are congruent.

-
All four angles are right angles.


Triangle Cent
ers

Angle Bisectors
-

Incenter







Perpendicular Bisectors
-

Circumcenter









Altitudes
-

Orthocenter







Medians
-

Centroid























Area of Polygons




Right Prism


LateralArea = Ph

SurfaceArea = Ph
-
2B

Volume =
Bh

Regular Pyramid




Pythagorean Theorem

a
2

+ b
2
= c
2

Right

a
2

+ b
2
> c
2

Acute

a
2

+ b
2
< c
2

Obtuse


Polyhedrons

Name

# of Faces

Tetrahedron

4

Hexahedron

6

Octahedron

8

Dodecahedron

12

Iscosahedron

20