9_GEOMETRY
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9_GEOMETRY
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124
Chapter 1: Vectors
Theory
Page 10
Section 1: Analysis of Vectors Geometrically
Theory
Page 10
Basic Vector Concepts
Theory
Page 10
Directed Line Segment
Theory
Page 10
Definition of a Vector
Theory
Page 11
Equal Vectors
Theory
Page 11
Vector Operations
Theory
Page 12
Addition of Vectors
Theory
Page 12
Subtraction of Vectors
Theory
Page 16
Multiplication of a Vector by a Scalar
Theory
Page 17
Parallel Vectors
Theory
Page 18
Non-Parallel Vectors
Theory
Page 19
Section 2: Analysis of Vectors Analytically
Theory
Page 24
Basic Concepts of Vectors in the Analytic Plane
Theory
Page 24
Axioms
Theory
Page 24
The Rectangular Coordinate System
Theory
Page 24
Position Vector
Theory
Page 25
Components of a Vector
Theory
Page 26
Equal Vectors
Theory
Page 27
Vector Operations
Theory
Page 28
Addition of Vectors
Theory
Page 28
Subtraction of Vectors
Theory
Page 29
Multiplication of a Vector by a Scalar
Theory
Page 30
Standard Base Vectors
Theory
Page 31
Parallel Vectors
Theory
Page 33
Section 3: The Dot Product of Two Vectors
Theory
Page 38
Dot Product
Theory
Page 38
Properties of the Dot Product
Theory
Page 38
Angle Between Two Vectors
Theory
Page 39
Perpendicular and Parallel Vectors
Theory
Page 41
Chapter 2: Congruence and Similarity
Theory
Page 56
Section 1: Congruence
Theory
Page 56
The Concept of Congruence
Theory
Page 56
Congruent Figures and Polygons
Theory
Page 56
Congruent Triangles
Theory
Page 57
The Triangle Angle Bisector Theorem
Theory
Page 64
Section 2: The Concept of Similarity
Theory
Page 67
Introduction to Similarity
Theory
Page 67
Similar Figures
Theory
Page 67
Similar Triangles
Theory
Page 67
Section 3: The Angle-Angle Similarity Postulate
Theory
Page 73
The Angle-Angle (AA) Similarity Postulate
Theory
Page 73
Section 4: Working with Similarity Triangles
Theory
Page 83
The Side-Angle-Side (SAS) Similarity Theorem
Theory
Page 83
The Side-Side-Side (SSS) Similarity Theorem
Theory
Page 85
The Triangle Proportionality Theorem and Thales’ Theorem
Theory
Page 90
The Triangle Proportionality Theorem
Theory
Page 90
Thales’ Theorem of Parallel Lines
Theory
Page 93
Further Applications
Theory
Page 95
Menelaus’ Theorem
Theory
Page 95
Ceva’s Theorem
Theory
Page 96
Section 5: Further Studies
Theory
Page 103
Euclidean Relations
Theory
Page 103
Median Relations
Theory
Page 106
Chapter 3: Circles
Theory
Page 126
Section 1: Basic Concepts
Theory
Page 126
Arc Length and the Circumference of a Circle
Theory
Page 126
Section 2: Angles and Circles
Theory
Page 132
Inscribed Angles and Arcs
Theory
Page 132
Angles Formed by Secants, Tangents and Chords
Theory
Page 148
Angles on a Circle
Theory
Page 148
Angles Inside a Circle
Theory
Page 152
Angles Outside a Circle
Theory
Page 159
Section 3: Segments and Circles
Theory
Page 174
Segments Formed by Secants and Chords
Theory
Page 174
The Power of a Point
Theory
Page 174
Segments Formed by Intersecting Secants
Theory
Page 175
Chapter 4: Trigonometric Theorems and Formulas
Theory
Page 196
Section 1: Trigonometric Theorems and Formulas
Theory
Page 196
Trigonometric Theorems
Theory
Page 196
The Law of Cosines
Theory
Page 196
The Law of Sines
Theory
Page 199
Chapter 5: Polygons
Theory
Page 206
Section 1: Introduction to Polygons
Theory
Page 206
Basic Concepts
Theory
Page 206
Simple and Closed Curves
Theory
Page 206
Definitions
Theory
Page 207
Convex and Concave Polygons
Theory
Page 209
Types of Polygon
Theory
Page 210
Diagonals in a Polygon
Theory
Page 212
Basic Properties of a Convex Polygon
Theory
Page 214
Number of Diagonals
Theory
Page 214
Angle Measures
Theory
Page 215
Regular Polygons
Theory
Page 220
Definition
Theory
Page 220
Basic Properties of a Regular Polygon
Theory
Page 221
Inscribed and Circumscribed Polygons
Theory
Page 226
Chapter 6: Areas of Regular Polygons and Circles
Theory
Page 238
Section 1: Areas of Regular Polygons and Circles
Theory
Page 238
Area of a Circular Region
Theory
Page 238
Area of a Sector
Theory
Page 242
Area of a Segment
Theory
Page 247
Area of a Ring
Theory
Page 250
Ratios in Circles
Theory
Page 252
Chapter 7: Space Geometry
Theory
Page 257
Section 1: Introduction to Space Geometry
Theory
Page 257
Lines and Planes in Space
Theory
Page 257
Determination of a Plane
Theory
Page 257
Mutual Positions of Two Lines in Space
Theory
Page 260
Mutual Positions of a Plane and a Line
Theory
Page 261
Mutual Positions of Two Planes
Theory
Page 269
Mutual Positions of Three Planes
Theory
Page 273
The Thales Theorem in Space
Theory
Page 276
Section 2: Perpendicularity
Theory
Page 284
Perpendicular Lines
Theory
Page 284
Line Perpendicular to a Plane
Theory
Page 285
Perpendicular Planes
Theory
Page 292
Distance
Theory
Page 293
Distance Between a Point and a Plane
Theory
Page 293
Distance Between a Plane and a Line Parallel to the Plane
Theory
Page 294
Distance Between Two Parallel Planes
Theory
Page 294
Distance Between Skew Lines
Theory
Page 295
Section 3: Solids with Curved Surfaces
Theory
Page 302
Some Important Polyhedrons
Theory
Page 302
Prisms
Theory
Page 302
Section 4: Volumes of Solids
Theory
Page 322
Circular Cylinder
Theory
Page 322
Areas of Cones
Theory
Page 325
Spheres
Theory
Page 327
Fundamental Definitions
Theory
Page 327
Section 5: Sections and Combinations of Solids
Theory
Page 332
Volume of a Right Prism
Theory
Page 332
Volume of a Pyramid
Theory
Page 333
Volumes of Cones
Theory
Page 338
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