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....................................................... 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