-PRE-GEOMETRY
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-PRE-GEOMETRY
Preparing book pages
1
Entries
222
Chapter 1: Geometric Concepts
Theory
Page 9
1.1 Basic Geometric Concepts
Theory
Page 10
Point, Line, and Plane
Theory
Page 10
Introduction
Theory
Page 10
Point
Theory
Page 11
Line
Theory
Page 11
Plane
Theory
Page 12
Collinear Points
Theory
Page 13
Line Segment, Ray, and Half Line
Theory
Page 14
Line Segment
Theory
Page 14
Ray
Theory
Page 16
Half Line
Theory
Page 16
Plane and Space
Theory
Page 16
Plane
Theory
Page 16
Space
Theory
Page 17
Relation Between Two Lines
Theory
Page 18
Intersecting Lines
Theory
Page 18
Parallel Lines
Theory
Page 18
Coincident Lines
Theory
Page 18
Skew Lines
Theory
Page 18
Relation Between a Line and a Plane
Theory
Page 19
The Intersection of a Line and a Plane
Theory
Page 19
Parallelism of a Line and a Plane
Theory
Page 19
A Line Lies in a Plane
Theory
Page 19
Relation Between Two Planes
Theory
Page 19
Parallel Planes
Theory
Page 19
Intersecting Planes
Theory
Page 19
Coincident Planes
Theory
Page 20
Half Planes
Theory
Page 20
Chapter Map
Other
Page 20
Chapter 1 Review Exercises
Problem
Page 23
Chapter 1 Review Test
Test
Page 24
Chapter 2: Angles
Theory
Page 25
2.1 Angles
Theory
Page 26
Regions of an Angle
Theory
Page 26
Angle
Theory
Page 26
Interior and Exterior Regions of an Angle
Theory
Page 26
Measuring Angles
Theory
Page 27
Types of Angle with Respect to Their Measures
Theory
Page 29
Acute Angle
Theory
Page 29
Right Angle
Theory
Page 30
Obtuse Angle
Theory
Page 30
Straight Angle
Theory
Page 30
Complete Angle
Theory
Page 30
Types of Angle with Respect to Their Position
Theory
Page 30
Adjacent Angles
Theory
Page 30
Vertical Angles
Theory
Page 31
Congruent Angles
Theory
Page 31
Types of Angle with Respect to the Sum of Their Measures
Theory
Page 31
Complementary Angles
Theory
Page 31
Supplementary Angles
Theory
Page 32
2.2 Angles Formed by a Transversal
Theory
Page 33
Corresponding Angles and Alternate Angles
Theory
Page 33
Corresponding Angles
Theory
Page 33
Alternate Interior Angles
Theory
Page 34
Alternate Exterior Angles
Theory
Page 34
Interior Angles on the Same Side of a Transversal
Theory
Page 35
Angles with Parallel Sides
Theory
Page 35
Bisector of an Angle
Theory
Page 39
Chapter Map
Other
Page 40
Chapter 2 Review Exercises
Problem
Page 42
Chapter 2 Review Test
Test
Page 44
Chapter 3: Triangles
Theory
Page 45
3.1 Triangles
Theory
Page 46
Basic Concepts
Theory
Page 46
Definition
Theory
Page 46
Angles of a Triangle
Theory
Page 46
Interior and Exterior Regions of a Triangle
Theory
Page 47
Intersection of a Triangle and a Line
Theory
Page 48
Types of Triangle
Theory
Page 50
Triangle Types Defined by Sides
Theory
Page 50
Triangle Types Defined by Angles
Theory
Page 50
Properties of the Angles and Sides of a Triangle
Theory
Page 53
Angles of a Triangle
Theory
Page 53
Relations Between the Angles and the Sides of a Triangle
Theory
Page 57
Exercises 3.1
Problem
Page 60
3.2 Congruent and Similar Triangles
Theory
Page 62
Congruent Triangles
Theory
Page 62
Concept of Congruence and Congruent Triangles
Theory
Page 62
Proving that Triangles are Congruent
Theory
Page 64
Similar Triangles
Theory
Page 66
Concept of Similarity
Theory
Page 66
Similar Triangles
Theory
Page 68
Proving that Triangles are Similar
Theory
Page 68
Examples and Applications
Theory
Page 72
Exercises 3.2
Problem
Page 75
3.3 Constructing Triangles
Theory
Page 77
Constructing a Triangle from Three Known Sides
Theory
Page 78
Constructing a Triangle from Two Known Angles and a Known Side
Theory
Page 78
Constructing a Triangle from Two Known Sides and a Known Angle
Theory
Page 79
3.4 Right Triangles
Theory
Page 81
The Pythagorean Theorem
Theory
Page 81
Isosceles Right Triangles (45°-45°-90° Triangles)
Theory
Page 82
30°-60°-90° Right Triangle
Theory
Page 83
The Euclidean Theorems
Theory
Page 84
Exercises 3.4
Problem
Page 87
3.5 Perimeter and Area of a Triangle
Theory
Page 88
Perimeter of a Triangle
Theory
Page 88
Area of a Triangle
Theory
Page 89
Chapter Map
Other
Page 93
Chapter 3 Review Exercises
Problem
Page 98
Chapter 3 Review Test A
Test
Page 101
Chapter 3 Review Test B
Test
Page 103
Chapter 4: Polygons
Theory
Page 105
4.1 Polygons
Theory
Page 106
Polygons and Their Properties
Theory
Page 106
Introducing Polygons
Theory
Page 106
Convex and Concave Polygons
Theory
Page 107
Types of Polygon
Theory
Page 108
Regular Polygons
Theory
Page 108
Diagonals of a Polygon
Theory
Page 108
Angles of a Polygon
Theory
Page 109
Interior Angles of a Polygon
Theory
Page 109
Exterior Angles of a Polygon
Theory
Page 111
Exercises 4.1
Problem
Page 113
4.2 Quadrilaterals
Theory
Page 114
Definition
Theory
Page 114
Angles of a Quadrilateral
Theory
Page 115
4.3 Types of Quadrilateral
Theory
Page 117
Parallelogram
Theory
Page 117
Properties of a Parallelogram
Theory
Page 117
Perimeter of a Parallelogram
Theory
Page 121
Area of a Parallelogram
Theory
Page 122
Rectangle
Theory
Page 125
Perimeter of a Rectangle
Theory
Page 126
Area of a Rectangle
Theory
Page 127
Square
Theory
Page 129
Perimeter of a Square
Theory
Page 130
Area of a Square
Theory
Page 130
Rhombus
Theory
Page 132
Perimeter of a Rhombus
Theory
Page 134
Area of a Rhombus
Theory
Page 134
Kite
Theory
Page 135
Perimeter of a Kite
Theory
Page 135
Area of a Kite
Theory
Page 135
Trapezoid
Theory
Page 136
Definition
Theory
Page 136
Properties of a Trapezoid
Theory
Page 136
Isosceles Trapezoid
Theory
Page 138
Right Trapezoid
Theory
Page 138
Perimeter of a Trapezoid
Theory
Page 138
Area of a Trapezoid
Theory
Page 139
Exercises 4.3
Problem
Page 141
Chapter Map
Other
Page 143
Chapter 4 Review Exercises
Problem
Page 147
Chapter 4 Review Test
Test
Page 149
Chapter 5: Circles
Theory
Page 151
5.1 Circles
Theory
Page 152
Basic Concepts
Theory
Page 152
Definition
Theory
Page 152
Regions Separated by a Circle in a Plane
Theory
Page 153
Auxiliary Elements of a Circle
Theory
Page 153
Relative Position of a Line and a Circle in the Same Plane
Theory
Page 154
Chords
Theory
Page 155
Tangents
Theory
Page 157
Relative Position of Two Circles in the Same Plane
Theory
Page 158
Exercises 5.1
Problem
Page 160
5.2 Arcs and Angles of a Circle
Theory
Page 161
Arcs and Central Angles
Theory
Page 161
Inscribed Angles
Theory
Page 162
Exercises 5.2
Problem
Page 168
5.3 Circumference and Area of a Circle
Theory
Page 169
Circumference and Arc Length
Theory
Page 169
Circumference of a Circle
Theory
Page 169
Arc Length
Theory
Page 170
Area of a Circle, a Sector, and a Segment
Theory
Page 171
Area of a Circle
Theory
Page 171
Area of an Annulus
Theory
Page 172
Area of a Sector
Theory
Page 173
Area of a Segment
Theory
Page 174
Exercises 5.3
Problem
Page 175
5.4 Basic Constructions
Theory
Page 177
Chapter Map
Other
Page 182
Chapter 5 Review Exercises
Problem
Page 185
Chapter 5 Review Test
Test
Page 187
Chapter 6: Trigonometry
Theory
Page 189
6.1 Trigonometric Ratios in a Right Triangle
Theory
Page 190
Trigonometric Ratios of Acute Angles
Theory
Page 190
Reciprocal Trigonometric Ratios
Theory
Page 192
Trigonometric Ratios of Complementary Angles
Theory
Page 192
Basic Trigonometric Identities
Theory
Page 193
Finding a Trigonometric Ratio from a Given Ratio
Theory
Page 196
Exercises 6.1
Problem
Page 199
6.2 Trigonometric Ratios of Some Special Triangles
Theory
Page 200
Ratios in 30°-60°-90° Triangle
Theory
Page 200
Ratios in 45°-45°-90° Triangle
Theory
Page 200
6.3 Using a Trigonometric Table
Theory
Page 202
Using a Table of Trigonometric Ratios
Theory
Page 202
The Ranges of Sine and Cosine
Theory
Page 202
6.4 Applications of Trigonometry
Theory
Page 204
Chapter Map
Other
Page 206
Chapter 6 Review Exercises
Problem
Page 208
Chapter 6 Review Test
Test
Page 209
Chapter 7: Measurements
Theory
Page 211
7.1 Measurements
Theory
Page 212
Basic Concepts
Theory
Page 212
Measurements of Length
Theory
Page 212
Metric Units of Length
Theory
Page 212
Converting Units of Length
Theory
Page 213
Measurements of Area
Theory
Page 215
Metric Units of Area
Theory
Page 215
Converting Units of Area
Theory
Page 215
Measuring Land Area
Theory
Page 216
Measurements of Volume
Theory
Page 218
Metric Units of Volume
Theory
Page 218
Converting Units of Volume
Theory
Page 218
Prisms
Theory
Page 219
Volume and Surface Area of Some Common Solids
Theory
Page 221
Measurements of Capacity and Mass
Theory
Page 224
Metric Units of Capacity
Theory
Page 224
Metric Units of Mass
Theory
Page 225
Measurements of Time
Theory
Page 226
Units of Time
Theory
Page 226
Chapter Map
Other
Page 228
Chapter 7 Review Exercises
Problem
Page 230
Chapter 7 Review Test
Test
Page 231
Answers to Practice Problems
Answer
Page 233
Answers to Exercises
Answer
Page 238
Answers to Review Exercises
Answer
Page 240
Answers to Review Tests
Answer
Page 242
Symbols
Other
Page 243
Glossary
Other
Page 244
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