Congruent Triangles

Geometry for Enjoyment and ChallengeTable of ContentsChapter 1: Introduction to Geometry1.1 Getting Started1.2 Measurement of Segments and Angles1.3 Collinearity, Betweeness, and Assumptions1.4 Beginning Proofs1.5 Division of Segments and Angles1.6 Paragraph Proofs1.7 Deductive Structure1.8 Statements of Logic1.9 ProbabilityChapter Summary

Chapter 2: Basic Concepts and Proofs2.1 Perpendicularity2.2 Complementary and Supplementary Angles2.3 Drawing Conclusions2.4 Congruent Supplements and Complements2.5 Addition and Subtraction Properties2.6 Multiplication and Division Properties2.7 Transitive and Substitution Properties2.8 Vertical AnglesChapter Summary

Chapter 3: Congruent Triangles3.1 What Are Congruent Figures?3.2 Three Ways to Prove Triangles Congruent3.3 CPCTC and Circles3.4 Beyond CPCTC3.5 Overlapping Triangles3.6 Types of Triangles3.7 Angle-Side Theorems3.8 The HL PostulateChapter SummaryCumulative Review: Chapters 1 - 3

Chapter 4: Lines in the Plane4.1 Detours and Midpoints4.2 The Case of the Missing Diagram4.3 A Right-Angle Theorem4.4 The Equidistance Theorems4.5 Introduction to Parallel Lines4.6 SlopeChapter Summary

Chapter 5: Parallel Lines and Related Figures5.1 Indirect Proof5.2 Proving That Lines are Parallel5.3 Congruent Angles Associated with Parallel Lines5.4 Four-Sided Polygons5.5 Properties of Quadrilaterals5.6 Proving That A Quadrilateral Is A Parallelogram5.7 Proving That Figures Are Special QuadrilateralsChapter Summary

Chapter 6: Lines and Planes in Space6.1 Relating Lines to Planes6.2 Perpendicularity of a Line and a Plane6.3 Basic Facts About Parallel PlanesChapter SummaryCumulative Review: Chapters 1 - 6

Chapter 7: Polygons7.1 Triangle Application Theorems7.2 Two Proof-Oriented Triangle Theorems7.3 Formulas Involving Polygons7.4 Regular PolygonsChapter Summary

Chapter 8: Similar Polygons8.1 Ratio and Proportion8.2 Similarity8.3 Methods of Proving Triangles Similar8.4 Congruences and Proportions in Similar Triangles8.5 Three Theorems Involving ProportionsChapter Summary

Chapter 9: The Pythagorean Theorem9.1 Review of Radicals and Quadratic Equations9.2 Introduction to Circles9.3 Altitude-On-Hypotenuse Theorems9.4 Geometry's Most Elegant Theorem9.5 The Distance Formula9.6 Families of Right Triangles9.7 Special Right Triangles9.8 The Pythagorean Theorem and Space Figures9.9 Introduction to Trigonometry9.10 Trigonometric RatiosChapter SummaryCumualtive Review: Chapters 1 - 9

Chapter 10: Circles10.1 The Circle10.2 Congruent Chords10.3 Arcs of a Circle10.4 Secants and Tangents10.5 Angles Related to a Circle10.6 More Angle-Arc Theorems10.7 Inscribed and Circumscribed Polygons10.8 The Power Theorems10.9 Circumference and Arc LengthChapter Summary

Chapter 11: Area11.1 Understanding Area11.2 Areas of Parallelograms and Triangles11.3 The Area of a Trapezoid11.4 Areas of Kites and Related Figures11.5 Areas of Regular Polygons11.6 Areas of Circles, Sectors, and Segments11.7 Ratios of Areas11.8 Hero's and Brahmagupta's FormulasChapter Summary

Chapter 12: Surface Area and Volume12.1 Surface Areas of Prisms12.2 Surface Areas of Pyramids12.3 Surface Areas of Circular Solids12.4 Volumes of Prisms and Cylinders12.5 Volumes of Pyramids and Cones12.6 Volumes of SpheresChapter SummaryCumulative Review: Chapters 1 - 12

Chapter 13: Coordinate Geometry Extended13.1 Graphing Equations13.2 Equations of Lines13.3 Systems of Equations13.4 Graphing Inequalities13.5 Three-Dimensional Graphing and Reflections13.6 Circles13.7 Coordinate-Geometry PracticeChapter Summary

Chaper 14: Locus and Constructions14.1 Locus14.2 Compound Locus14.3 The Concurrence Theorems14.4 Basic Constructions14.5 Applications of the Basic Constructions14.6 Triangle ConstructionsChapter Summary

Chapter 15: Inequalities15.1 Number Properties15.2 Inequalities in a Triangle15.3 The Hinge TheoremsChapter SummaryCumulative Review: Chapters 1 - 15

Chapter 16: Enrichment Topics16.1 The Point-Line Distance Formula16.2 Two Other Useful Formulas16.3 Stewart's Theorem16.4 Ptolemy's Theorem16.5 Mass Points16.6 Inradius and Circumradius Formulas16.7 Formulas For Your To DevelopChapter Summary

List of Postulates and TheoremsSelected AnswersGlossaryIndexSymbols Used in Geometry