Geometrija

Copyright 2010‐2015, Earl Whitney, Reno NV.  All Rights Reserved 

Math Handbook 

of Formulas, Processes and Tricks 

Geometry 

Prepared by:  Earl L. Whitney, FSA, MAAA 

Version 2.9 

November 26, 2015 

Page

Description

Chapter

1:

Basics

6

Points,

Lines

&

Planes

7

Segments,

Rays

&

Lines

8

Distance

Between

Points

(1

‐

Dimensional,

2

‐

Dimensional)

9

Distance

Formula

in

“n”

Dimensions

10

Angles

11

Types

of

Angles

Chapter

2:

Proofs

12

Conditional

Statements

(Original,

Converse,

Inverse,

Contrapositive)

13

Basic

Properties

of

Algebra

(Equality

and

Congruence,

Addition

and

Multiplication)

14

Inductive

vs.

Deductive

Reasoning

15

An

Approach

to

Proofs

Chapter

3:

Parallel

and

Perpendicular

Lines

16

Parallel

Lines

and

Transversals

17

Multiple

Sets

of

Parallel

Lines

18

Proving

Lines

are

Parallel

19

Parallel

and

Perpendicular

Lines

in

the

Coordinate

Plane

Chapter

4:

Triangles

 ‐ 

Basic

20

Types

of

Triangles

(Scalene,

Isosceles,

Equilateral,

Right)

21

Congruent

Triangles

(SAS,

SSS,

ASA,

AAS,

CPCTC)

22

Centers

of

Triangles

23

Length

of

Height,

Median

and

Angle

Bisector

24

Inequalities

in

Triangles

Chapter

5:

Polygons

25

Polygons

–

Basic

(Definitions,

Names

of

Common

Polygons)

26

Polygons

–

More

Definitions

(Definitions,

Diagonals

of

a

Polygon)

27

Interior

and

Exterior

Angles

of

a

Polygon

Geometry

Handbook

Table

of

Contents

Version 2.9

Page 2 of 82

November 26, 2015

Geometry

Handbook

Table

of

Contents

Page

Description

Chapter

10:

Circles

58

Parts

of

a

Circle

59

Angles

and

Circles

Chapter

11:

Perimeter

and

Area

60

Perimeter

and

Area

of

a

Triangle

61

More

on

the

Area

of

a

Triangle

62

Perimeter

and

Area

of

Quadrilaterals

63

Perimeter

and

Area

of

General

Polygons

64

Circle

Lengths

and

Areas

65

Area

of

Composite

Figures

Chapter

12:

Surface

Area

and

Volume

66

Polyhedra

67

A

Hole

in

Euler’s

Theorem

68

Platonic

Solids

69

Prisms

70

Cylinders

71

Surface

Area

by

Decomposition

72

Pyramids

73

Cones

74

Spheres

75

Similar

Solids

76

Summary

of

Perimeter

and

Area

Formulas

–

2D

Shapes

77

Summary

of

Surface

Area

and

Volume

Formulas

–

3D

Shapes

78

Index

Version 2.9

Page 4 of 82

November 26, 2015

Geometry

Handbook

Table

of

Contents

Useful

Websites

mathworld.wolfram.com/

www.mathguy.us

www.cde.ca.gov/ta/tg/sr/documents/rtqgeom.pdf

Schaum’s

Outlines

An

important

student

resource

for

any

high

school

math

student

is

a

Schaum’s

Outline.

Each

book

in

this

series

provides

explanations

of

the

various

topics

in

the

course

and

a

substantial

number

of

problems

for

the

student

to

try.

Many

of

the

problems

are

worked

out

in

the

book,

so

the

student

can

see

examples

of

how

they

should

be

solved.

Schaum’s

Outlines

are

available

at

Amazon.com,

Barnes

&

Noble

and

other

booksellers.

Wolfram

Math

World

–

Perhaps

the

premier

site

for

mathematics

on

the

Web.

This

site

contains

definitions,

explanations

and

examples

for

elementary

and

advanced

math

topics.

Mathguy.us

–

Developed

specifically

for

math

students

from

Middle

School

to

College,

based

on

the

author's

extensive

experience

in

professional

mathematics

in

a

business

setting

and

in

math

tutoring.

Contains

free

downloadable

handbooks,

PC

Apps,

sample

tests,

and

more.

California

Standard

Geometry

Test

–

A

standardized

Geometry

test

released

by

the

state

of

California.

A

good

way

to

test

your

knowledge.

Version 2.9

Page 5 of 82

November 26, 2015

Chapter

1

Basic

Geometry

Geometry

Segments,

Rays

&

Lines

Some

Thoughts

About

…

Line

Segments



Line

segments

are

generally

named

by

their

endpoints,

so

the

segment

at

right

could

be

named

either

or

.



Segment

contains

the

two

endpoints

(

A

and

B

)

and

all

points

on

line

that

are

between

them.

Rays



Rays

are

generally

named

by

their

single

endpoint,

called

an

initial

point

,

and

another

point

on

the

ray.



Ray

contains

its

initial

point

A

and

all

points

on

line

in

the

direction

of

the

arrow.



Rays

and

are

not

the

same

ray.



If

point

O

is

on

line

and

is

between

points

A

and

B

,

then

rays

and

are

called

opposite

rays

.

They

have

only

point

O

in

common,

and

together

they

make

up

line

.

Lines



Lines

are

generally

named

by

either

a

single

script

letter

(e.g.,

l

)

or

by

two

points

on

the

line

(e.g.,.

).



A

line

extends

infinitely

in

the

directions

shown

by

its

arrows.



Lines

are

parallel

if

they

are

in

the

same

plane

and

they

never

intersect.

Lines

f

and

g

,

at

right,

are

parallel.



Lines

are

perpendicular

if

they

intersect

at

a

90

⁰ 

angle.

A

pair

of

perpendicular

lines

is

always

in

the

same

plane.

Lines

f

and

e

,

at

right,

are

perpendicular.

Lines

g

and

e 

are

also

perpendicular.



Lines

are

skew

if

they

are

not

in

the

same

plane

and

they

never

intersect.

Lines

k

and

l

,

at

right,

are

skew.

(Remember

this

figure

is

3

‐

dimensional.)

Version 2.9

Page 7 of 82

November 26, 2015