The Complete Idiot's Guide to Geometry

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Penguin, 2004 - Mathematics - 376 pages
Geometry is hard. This book makes it easier. You do the math. This is the fourth title in the series designed to help high school and college students through a course they'd rather not be taking. A non-intimidating, easy- to-understand companion to their textbook, this book takes students through the standard curriculum of topics, including proofs, polygons, coordinates, topology, and much more.
 

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Contents

The Foundation
1
What Is Geometry Anyway?
3
Whats the Point?
4
Getting Into Shape
5
Learning How to Write Proofs
6
And the Winner Is Euclid
7
A Goliath Mathematician
9
Can I Really Learn This?
10
Opening Doors with Similar Triangles
167
The Pythagorean Theorem
168
Parallel Segments and Segment Proportions
170
Three Famous Triangles
173
306090 Triangle
174
454590 Triangle
176
Putting Quadrilaterals in the Forefront
179
Properties of All Quadrilaterals
180

Lets Do Algebra
13
Long Lost Relations
14
Properties of Equality
15
Reflexive Symmetric and Transitive Properties
16
Algebraic Properties of Equality
17
The Square Root Property of Equality
19
Properties of Inequality
20
Is It an Equivalence Relation?
21
An Additional Additive Property
22
Building Blocks
25
Coming to Terms
26
Lines
28
Line Segments
29
Segment Length
30
A New Relation
31
Segment Addition
32
Rays
33
Planes
34
Theres Always an Angle
37
Whats in a Name?
38
Are You My Type? The Basic Angle Classifications
40
Angle Addition
41
How Do Angles Relate? Classifying Pairs of Angles
42
Congruent Angles
43
Complementary and Supplementary Angles
44
A First Look at Proving Angle Congruence
46
Lines and the Angles They Form
49
Linear Interactions
50
Perpendicular Lines
52
Euclids 5th
55
Transversals and the New Angle Pairs
57
A Polygon Is a ManySided Thing
59
Coming to Terms with the Terminology
60
Naming Conventions and Classifications
63
The Interior Angles
64
Regular Polygons
67
Introducing Proofs
71
Logic Rules for Arguing
73
Inductive Reasoning
74
Elementary My Dear Watson
75
Logical Constructions and Truth Tables
76
Conjunction
77
Disjunction
78
Implication or Conditional
79
Logical Equivalence and Tautology
81
Taking the Burden out of Proofs
85
The Law of Detachment
86
The Importance of Being Direct
87
The Advantage of Being Indirect
89
Use It or Lose It
90
What Should You Bring to a Formal Proof?
92
Proving Segment and Angle Relationships
97
Exploring Midpoints
98
How Many Midpoints Are There?
99
Proving Angles Are Congruent
101
Using and Proving Angle Complements
102
Using and Proving Angle Supplements
105
Proving Relationships Between Lines
109
Proofs Involving Perpendicular Lines
110
Lets Get Parallel
112
Proofs About Alternate Angles
113
Parallel Lines and Supplementary Angles
115
Using Parallelism to Prove Perpendicularity
116
Proving Lines Are Parallel
117
Piecing Together Triangles and Quadrilaterals
123
Twos Company Threes a Triangle
125
A Formal Introduction
126
Sums of Interior Angles Are Cooking at 180
128
Exterior Angle Relationships
130
Size Matters So Lets Measure
132
The Pythagorean Theorem
134
The Triangle Inequality
135
Congruent Triangles
139
CPOCTAC
140
The SSS Postulate
141
The SAS Postulate
142
The ASA Postulate
144
The AAS Theorem
145
The HL Theorem for Right Triangles
146
Proving Segments and Angles Are Congruent
149
Proving Lines Are Parallel
150
Similar Triangles
155
Ratio Proportion and Geometric Means
156
Properties of Similar Triangles
159
The Big Three
161
The SAS and SSS Similarity Theorems
164
Lets All Fly a Kite
182
Properties of Parallelograms
184
The Most Popular Parallelograms
186
Rhombuses
187
Squares
189
Area of Parallelograms
190
The Pythagorean Theorem again
191
Proofs About Quadrilaterals
195
When Is a Quadrilateral a Parallelogram?
196
Two Pairs of Congruent Sides
197
Two Pairs of Congruent Angles
199
Bisecting Diagonals
200
When Is a Parallelogram a Rectangle?
201
When Is a Parallelogram a Rhombus?
202
When Is a Parallelogram a Square?
204
Going Around in Circles
207
Anatomy of a Circle
209
Basic Terms
210
Arcs
211
Pi Anyone?
215
Tangents
217
From One Theorem Comes Many
218
Segments and Angles
225
Angles and Chords
226
Arcs and Chords
227
Radii and Chords
229
Putting the Pieces Together
233
Circular Arguments
237
Angles and Arcs
238
Similarity
241
Parallel Chords and Arcs
245
Putting Your Problems Behind You
247
The Unit Circle and Trigonometry
251
The Tangent Ratio
252
The Sine Ratio
255
The Cosine Ratio
257
And the Rest
259
How Does This Relate to the Unit Circle?
261
Where Can We Go from Here?
267
The Next Dimension Surfaces and Solids
269
Prisms
270
Pyramids
273
Cylinders and Cones
274
Polyhedra
276
Spheres
277
Platonic Solids
278
Under Construction
281
Tools of the Trade
282
Compass
283
Bisection
284
Bisecting Angles
285
Constructing Lines
287
Parallel Lines
289
Constructing Quadrilaterals
290
Parallelograms
291
Squares
292
When Geometry and Algebra Intersect
293
The Cartesian Coordinate System
294
Finding Horizontal and Vertical Distances
295
The Pythagorean Theorem Goes the Distance
296
The Midpoint Formula
297
Finding Equations of Lines
298
The PointSlope Formula
300
The Secret Lives of Parallel and Perpendicular Lines
301
A Picture Is Worth a Thousand Words
302
Whose Geometry Is It Anyway?
305
NonEuclidean Geometry
306
Saddle Up
307
Spherical Geometry
309
TaxiCab Geometry
310
Max Geometry
312
How Many Shapes Can a Circle Have?
313
Transformations
317
Isometrics
318
Translations
319
Reflections
320
Rotations
322
Glide Reflections
324
Dilations
325
Symmetry
326
Answer Key
331
Postulates and Theorems
351
Formulas
357
Glossary
359
Index
367
Copyright

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About the author (2004)

Denise Szecsei, Ph.D., is an assistant professor of mathematics at Stetson University where she teaches finite mathematics, mathematical modeling, and geometry, as well as a variety of liberal arts mathematics classes. Professor Szecsei developed a geometry class for liberal arts students and elementary education majors and has taught this class over the last three years, giving her firsthand knowledge of how to explain the concepts of geometry to those whose career paths will likely have little to do with the subject.

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