Table of Contents
Introduction 1
Common Core State Standards for Mathematics (CCSSM) 1
Connecting to Common Core Mathematics 2
Why You Need This Book 3
How to Use This Book 3
Hundreds of Practice Questions Online! 4
Chapter 1 Fundamental Ideas 5
Points, Lines, and Planes 6
Point 6
Line 6
Plane 7
Set 7
Postulates and Theorems 7
Segments, Midpoints, and Rays 9
Line segment 9
Midpoint 10
Ray 11
Angles 11
Adjacent angles 13
Circles 13
Central angles, sectors, and arcs 13
Special Angles 15
Right angle 15
Acute angle 15
Obtuse angle, 16
Complementary angles 17
Supplementary angles 18
Parallel, Intersecting, and Perpendicular Lines 19
Parallel lines in a plane 19
Intersecting lines 19
Perpendicular lines 20
Angle bisector and perpendicular bisector 21
Triangles, Quadrilaterals, and Polygons 21
Special triangles and quadrilaterals 23
Chapter 2 Basic Rigid Motions 25
Rotations 26
Counterclockwise rotation p of θ degrees around O 26
Clockwise rotation p of θ degrees around O 26
Transversals 30
Reflections 36
Translations 37
Chapter 3 Triangles and Congruence 41
Exterior Angle of a Triangle 42
Angle Sum of a Triangle 44
Classifying Triangles by Sides or Angles 44
Special names for sides and angles 45
Altitudes, Medians, and Angle Bisectors 46
Base and altitude 46
Median 47
Angle bisector 48
Special Features of Isosceles Triangles 48
Triangle Inequalities Regarding Sides and Angles 51
The Triangle Inequality Theorem 52
The Concept of Congruence 53
Corresponding Parts of Triangles 55
Congruence theorems of triangles 55
Chapter 4 Polygons 65
Triangulation of a Polygon and the Sum of the Interior Angles 65
Exterior Angles of a Convex Polygon 67
Regular Polygons 69
Parallelograms 70
Rectangles 72
Rhombus 72
Trapezoids 74
The Midpoint Theorem 77
Concurrence Theorems 78
Chapter 5 Similarity 83
Dilation 84
The Fundamental Theorem of Similarity 85
The Definition of Similarity 88
Similar Triangles 89
Applications of Similarity 92
Proportional Parts of Similar Triangles 97
Pythagorean Theorem 98
Chapter 6 Circles 103
Parts of Circles 103
Arcs 104
Arcs and Inscribed Angles 110
Concyclic Points 117
Segments of Intersecting Chords and Tangenrs 121
Chapter 7 Length and Area 127
Length of a Line Segment 128
Length of a Polygonal Curve 129
Squares and Rectangles 130
Triangles 134
Right triangles 134
Arbitrary triangles 135
Parallelograms 137
Trapezoids 138
Regular Polygons 140
Parts of a regular polygon 140
Finding the perimeter 141
Finding the area 141
Effect of a dilation of scale factor r on the area of a polygon 142
Area and Circumference of a Circle 143
Summary of Perimeter, Circumference, and Area Formulas 148
Chapter 8 Geometric Solids 151
Prisms 151
Right Prisms 152
Lateral area of a right prism 152
Total surface area of a right prism 153
Interior space of a solid 154
Right Circular Cylinders 156
Pyramids 158
Regular pyramids 158
Right Circular Cones 161
Spheres 164
Summary of Lateral Area, Total Area, and Volume Formulas 165
Chapter 9 Coordinate Geometry 167
One-Dimensional Distance Formula 171
Two-Dimensional Distance Formula 171
Midpoint Formula for One-Dimensional Space 174
Midpoint Formula for Two-Dimensional Space 174
Equation of a Circle 176
Lines on a Coordinate Plane 178
The Slope Theorem 180
Slopes of parallel lines 184
Slopes of perpendicular lines 187
Linear Equations in x and y 190
Summary of Coordinate Geometry Formulas 199
Review Questions 201
Glossary 213
Appendix: Postulates and Theorems 221
Postulates 221
Theorems 222
Chapter 1 Fundamental Ideas 222
Chapter 2 Basic Rigid Motions 223
Chapter 3 Triangles and Congruence 224
Chapter 4 Polygons 226
Chapter 5 Similarity 227
Chapter 6 Circles 229
Chapter 7 Length and Area 231
Chapter 8 Geometric Solids 232
Chapter 9 Coordinate Geometry 234
Index 237
