Math Handbook of Formulas, Processes and Tricks

Math Handbook

of Formulas, Processes and Tricks

(mathguy.us)

Geometry

Prepared by: Earl L. Whitney, FSA, MAAA

Version 4.2

August 26, 2023

Copyright 2010-2023, Earl Whitney, Reno NV. All Rights Reserved

Geometry Handbook

Table of Contents

Page

Description

6

7

8

8

9

11

12

13

14

Chapter 1: Basics

Points, Lines & Planes

Segments, Rays & Lines

Distance Between Points in 1 Dimension

Distances Between Collinear Points

Distance Between Points in 2 Dimensions

Partial Distances and Distance Equations

Distance Formula in ¡°n¡± Dimensions

Angles

Types of Angles

16

17

18

19

Chapter 2: Proofs

Conditional Statements (Original, Converse, Inverse, Contrapositive)

Basic Properties of Algebra (Equality and Congruence, Addition and Multiplication)

Inductive vs. Deductive Reasoning

An Approach to Proofs

22

23

24

25

27

Chapter 3: Parallel and Perpendicular Lines

Parallel Lines and Transversals

Multiple Sets of Parallel Lines

Proving Lines are Parallel

Parallel and Perpendicular Lines in the Coordinate Plane

Proportional Segments

29

31

35

37

40

42

Chapter 4: Triangles - Basic

What Makes a Triangle?

Inequalities in Triangles

Types of Triangles (Scalene, Isosceles, Equilateral, Right)

Congruent Triangles (SAS, SSS, ASA, AAS, HL, CPCTC)

Centers of Triangles

Length of Height, Median and Angle Bisector

43

44

45

Chapter 5: Polygons

Polygons ¨C Basic (Definitions, Names of Common Polygons)

Polygons ¨C More Definitions (Definitions, Diagonals of a Polygon)

Interior and Exterior Angles of a Polygon

Cover art by Rebecca Williams,

Twitter handle: @jolteonkitty

Version 4.2

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Geometry Handbook

Table of Contents

Page

Description

46

47

48

52

53

54

Chapter 6: Quadrilaterals

Definitions of Quadrilaterals

Figures of Quadrilaterals

Amazing Property of Quadrilaterals

Characteristics of Parallelograms

Parallelogram Proofs (Sufficient Conditions)

Kites and Trapezoids

55

57

59

61

63

65

Chapter 7: Transformations

Introduction to Transformation

Reflection

Rotation

Translation

Compositions

Rotation About a Point Other than the Origin

68

69

70

71

73

74

75

78

Chapter 8: Similarity

Ratios Involving Units

Similar Polygons

Scale Factor of Similar Polygons

Dilations of Polygons

More on Dilation

Similar Triangles (SSS, SAS, AA)

Proportion Tables for Similar Triangles

Three Similar Triangles

80

81

83

85

86

87

90

91

Chapter 9: Right Triangles

Pythagorean Theorem

Pythagorean Triples

Special Triangles (45?-45?-90? Triangle, 30?-60?-90? Triangle)

Trigonometric Functions and Special Angles

Trigonometric Function Values in Quadrants II, III, and IV

Graphs of Trigonometric Functions

Vectors

Operating with Vectors

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Geometry Handbook

Table of Contents

Page

Description

92

93

94

95

95

97

Chapter 10: Circles

Parts of a Circle

Angles, Arcs, and Segments

Circle Vocabulary

Facts about Circles

Facts about Chords

Facts about Tangents

98

100

101

102

106

108

Chapter 11: Perimeter and Area

Perimeter and Area of a Triangle

More on the Area of a Triangle

Perimeter and Area of Quadrilaterals

Perimeter and Area of Regular Polygons

Circle Lengths and Areas

Area of Composite Figures

111

112

113

114

116

118

119

121

123

125

Chapter 12: Surface Area and Volume

Polyhedra

A Hole in Euler¡¯s Theorem

Platonic Solids

Prisms

Cylinders

Surface Area by Decomposition

Pyramids

Cones

Spheres

Similar Solids

127

129

Appendix A: Geometry Formulas

Appendix B: Trigonometry Formulas

131

Index

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Geometry Handbook

Table of Contents

Useful Websites

Wolfram Math World ¨C Perhaps the premier site for mathematics on the Web. This site contains

definitions, explanations and examples for elementary and advanced math topics.

mathworld.

Mathguy.us ¨C 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.

mathguy.us

Broken Arrow, Oklahoma Standard Geometry Test ¨C A standardized Geometry test released by the

state of Oklahoma. A good way to test your knowledge.

pages/uploaded_files/Geometry%20Practice%20Test.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 , Barnes & Noble and

other booksellers.

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