Geometry Formulas

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 9 μήνες)

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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

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

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

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