The Essential Guide to GEOMETRY

Preface 2
저자 소개 3
이 책의 구성과 특징 4
Topic 1 Basic Elements of Geometry
1.1 Points, Lines, and Planes................................................... 10
1.2 Collinear or Coplanar Points.............................................. 11
1.3 Line, Segment, and Ray..................................................... 12
1.4 Midpoint and Bisector of a Segment.................................. 14
1.5 Coordinate Plane................................................................ 16
1.6 Angle and Its Measure....................................................... 18
1.7 Congruent Angles.............................................................. 19
1.8 Bisector of an Angle.......................................................... 20
1.9 Angle Relationship............................................................ 21

Topic 2 Relationship between Point, Line, and Plane
2.1 Point and Line.................................................................... 24
2.2 Two Lines on a Plane......................................................... 25
2.3 What forms a Plane?.......................................................... 26
2.4 Two Lines in a Space......................................................... 27
2.5 Plane and Line in a Space.................................................. 28
2.6 Plane and Plane in a Space................................................. 29
2.7 Summary : Postulates about Points, Lines, and Planes...... 30

Topic 3 Mathematical Reasoning
3.1 Induction and Deduction.................................................... 32
3.2 Truth Tables....................................................................... 33
3.3 Tools for Deduction : Law of Detachment and of Syllogism. 36
3.4 Algebraic Proof and Geometric Proof................................ 37
3.5 Proving Segment Relationships......................................... 38
3.6 Proving Angle Relationships.............................................. 40

Topic 4 Parallel and Perpendicular Lines
4.1 Parallel Lines and Transversal........................................... 48
4.2 Parallel Line Property........................................................ 49
4.3 Slope of Lines.................................................................... 52
4.4 Proof about Parallel Lines.................................................. 54
4.5 Distance Formula Revisited............................................... 57

Topic 5 Congruent Triangles
5.1 Basic Classification of Triangles........................................ 60
5.2 Interior Angle Sum / Exterior Angle Theorem................... 61
5.3 Congruent Triangles........................................................... 63
5.4 Congruence Postulates....................................................... 65
5.5 Finding Congruent Triangles in Isosceles Triangle............ 69

Topic 6 Triangle Properties............................................... 73
6.1 Angle Bisector Theorem.................................................... 74
6.2 Points of Concurrency....................................................... 76
6.3 Properties of Right Triangle............................................... 81
6.4 Triangular Inequality......................................................... 83

Topic 7 Similar Triangles
7.1 Similar Triangles................................................................ 88
7.2 Attacking Similar Triangle Problems................................. 90
7.3 Ratio of Similar Figures..................................................... 92

Topic 8 Quadrilateral
8.1 Quadrilateral...................................................................... 94
8.2 Trapezoid........................................................................... 95
8.3 Parallelogram..................................................................... 97
8.4 Rhombus............................................................................ 99
8.5 Rectangle........................................................................... 101
8.6 Square................................................................................ 103

Topic 9 Polygons
9.1 Polygon.............................................................................. 106
9.2 Finding Angles................................................................... 107
9.3 Area of Polygon................................................................. 109
9.4 Diagonals of Polygons....................................................... 113

Topic 10 Circles
10.1 Terminology....................................................................... 116
10.2 Arcs, Angles and Chords.................................................... 117
10.3 Power of a Point Theorem................................................. 127

Topic 11 Transformation
11.1 Translation......................................................................... 130
11.2 Rotation............................................................................. 132
11.3 Reflection........................................................................... 135
11.4 Dilation.............................................................................. 138
Topic 12 Solid Figures
12.1 Polyhedron......................................................................... 142
12.2 Solid of Revolution............................................................ 144
Topic 13 Surface Area and Volume
13.1 Surface Area...................................................................... 150
13.2 Volume............................................................................... 153
Topic 14 Trigonometric Ratio
14.1 Basic Ratio......................................................................... 156
14.2 Extension of Basic Ratio.................................................... 158

Solution to 120 Exercises 161