Geometry

Course Info

Table of Contents

Chapter 1 – LINE AND ANGLE RELATIONSHIPS

  • 1.1  Sets, Statements and Reasoning
  • 1.2  Informal Geometry and Measurement
  • 1.3  Early Definitions and Postulates
  • 1.4  Angles and Their Relationships
  • 1.5  Introduction to Geometric Proof
  • 1.6  Relationships: Perpendicular Lines
  • 1.7  The Formal Proof of a Theorem

Chapter 2 – PARALLEL LINES

  • 2.1  The Parallel Postulate and Special Angles
  • 2.2  Indirect Proof
  • 2.3  Proving Lines Parallel
  • 2.4  The Angles of a Triangle
  • 2.5  Convex Polygons
  • 2.6  Symmetry and Transformations

Chapter 3 – TRIANGLES

  • 3.1  Congruent Triangles
  • 3.2  Corresponding Parts of Congruent Triangles
  • 3.3  Isosceles Triangles
  • 3.4  Basic Constructions Justified
  • 3.5  Inequalities in a Triangle

Chapter 4 – QUADRILATERALS

  • 4.1  Properties of a Parallelogram
  • 4.2  The Parallelogram and Kite
  • 4.3  The Rectangle, Square, and Rhombus
  • 4.4  The Trapezoid

Chapter 5 – SIMILAR TRIANGLES

  • 5.1  Ratios, Rates, and Proportions
  • 5.2  Similar Polygons
  • 5.3  Proving Triangles Similar
  • 5.4  The Pythagorean Theorem
  • 5.5  Special Right Triangles
  • 5.6  Segments Divided Proportionately

Chapter 6 – CIRCLES

  • 6.1  Circles and Related Segments and Angles
  • 6.2  More Angle Measures in the Circle
  • 6.3  Line and Segment Relationships in the Circle
  • 6.4  Some Constructions and Inequalities for the Circle

Chapter 7 – LOCUS AND CONCURRENCE

  • 7.1  Locus of Points
  • 7.2  Concurrence of Lines
  • 7.3  More About Regular Polygons

Chapter 8 – AREAS OF POLYGONS AND CIRCLES

  • 8.1  Area and Initial Postulates
  • 8.2  Perimeter and Area of Polygons
  • 8.3  Regular Polygons and Area
  • 8.4  Circumference and Area of a Circle
  • 8.5  More Area Relationships in the Circle

Chapter 9 – SURFACES AND SOLIDS

  • 9.1  Prisms, Area, and Volume
  • 9.2  Pyramids, Area, and Volume
  • 9.3  Cylinders and Cones
  • 9.4  Polyhedrons and Spheres

Chapter 10 – ANALYTIC GEOMETRY

  • 10.1  The Rectangular Coordinate System
  • 10.2  Graphs of Linear Equations and Slope
  • 10.3  Preparing to do Analytic Proofs
  • 10.4  Analytic Proofs
  • 10.5  Equations of Lines

Chapter 11 – INTRODUCTION TO TRIGONOMETRY

  • 11.1  The Sine Ratio and Applications
  • 11.2  The Cosine Ratio and Applications
  • 11.3  The Tangent Ratio and Other Ratios
  • 11.4  Applications with Acute Triangles

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