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
Page 2 of 137
August 26, 2023
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
Version 4.2
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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 Eulers 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
Version 4.2
Page 4 of 137
August 26, 2023
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
Schaums Outlines
An important student resource for any high school math student is a
Schaums 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.
Schaums Outlines are available at , Barnes & Noble and
other booksellers.
Version 4.2
Page 5 of 137
August 26, 2023
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