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Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery.
Author Bio
Daniel C. Alexander has taught mathematics at Parkland College in Champagne, Illinois, for the past fifteen years. Prior to his arrival at Parkland, Professor Alexander taught at the high-school level. He received his undergraduate and graduate degrees at Southern Illinois, Carbondale.
Geralyn Koeberlein teaches mathematics at Mahomet-Seymour High School in Champagne, Illinois. She has been awarded several outstanding teacher awards throughout her 34 year career teaching at Mahomet-Seymour HS.
Note: Each chapter concludes with a Summary, Review Exercises, and a Chapter Test. 1. LINE AND ANGLE RELATIONSHIPS. Sets, Statements, and Reasoning. Informal Geometry and Measurement. Early Definitions and Postulates. Angles and Their Relationships. Introduction to Geometric Proof. Relationships: Perpendicular Lines. The Formal Proof of a Theorem. Perspective on History: The Development of Geometry. Perspective on Application: Patterns. 2. PARALLEL LINES. The Parallel Postulate and Special Angles. Indirect Proof. Proving Lines Parallel. The Angles of a Triangle. Convex Polygons. Symmetry and Transformations. Perspective on History: Sketch of Euclid. Perspective on Application: Non-Euclidean Geometries. 3. TRIANGLES. Congruent Triangles. Corresponding Parts of Congruent Triangles. Isosceles Triangles. Basic Constructions Justified. Inequalities in a Triangle. Perspective on History: Sketch of Archimedes. Perspective on Application: Pascal's Triangle. 4. QUADRILATERALS. Properties of a Parallelogram. The Parallelogram and Kite. The Rectangle, Square, and Rhombus. The Trapezoid. Perspective on History: Sketch of Thales. Perspective on Application: Square Numbers as Sums. 5. SIMILAR TRIANGLES. Ratios, Rates, and Proportions. Similar Polygons. Proving Triangles Similar. The Pythagorean Theorem. Special Right Triangles. Segments Divided Proportionally. Perspective on History: Ceva's Theorem. Perspective on Application: An Unusual Application of Similar Triangles. 6. CIRCLES. Circles and Related Segments and Angles. More Angle Measures in the Circle. Line and Segment Relationships in the Circle. Some Constructions and Inequalities for the Circle. Perspective on History: Circumference of the Earth. Perspective on Application: Sum of the Interior Angles of a Polygon. 7. LOCUS AND CONCURRENCE. Locus of Points. Concurrence of Lines. More About Regular Polygons. Perspective on History: The Value of Perspective on Application: The Nine-Point Circle. 8. AREAS OF POLYGONS AND CIRCLES. Area and Initial Postulates. Perimeter and Area of Polygons. Regular Polygons and Area. Circumference and Area of a Circle. More Area Relationships in the Circle. Perspective on History: Sketch of Pythagoras. Perspective on Application: Another Look at the Pythagorean Theorem. 9. SURFACES AND SOLIDS. Prisms, Area, and Volume. Pyramids, Area, and Volume. Cylinders and Cones. Polyhedrons and Spheres. Perspective on History: Sketch of Rene Descartes. Perspective on Application: Birds in Flight. 10. ANALYTIC GEOMETRY. The Rectangular Coordinate System. Graphs of Linear Equations and Slope. Preparing to do Analytic Proofs. Analytic Proofs. Equations of Lines. Perspective on History: The Banach-Tarski Paradox. Perspective on Application: The Point-of-Division Formulas. 11. INTRODUCTION TO TRIGONOMETRY. The Sine Ratio and Applications. The Cosine Ratio and Applications. The Tangent Ratio and Other Ratios. Applications with Acute Triangles. Perspective on History: Sketch of Plato. Perspective on Application: Radian Measure of Angles. APPENDICES. Appendix A: Algebra review. Appendix B: Summary of Constructions, Postulates, and Theorems and Corollaries.
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Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery.
Author Bio
Daniel C. Alexander has taught mathematics at Parkland College in Champagne, Illinois, for the past fifteen years. Prior to his arrival at Parkland, Professor Alexander taught at the high-school level. He received his undergraduate and graduate degrees at Southern Illinois, Carbondale.
Geralyn Koeberlein teaches mathematics at Mahomet-Seymour High School in Champagne, Illinois. She has been awarded several outstanding teacher awards throughout her 34 year career teaching at Mahomet-Seymour HS.
Table of Contents
Note: Each chapter concludes with a Summary, Review Exercises, and a Chapter Test. 1. LINE AND ANGLE RELATIONSHIPS. Sets, Statements, and Reasoning. Informal Geometry and Measurement. Early Definitions and Postulates. Angles and Their Relationships. Introduction to Geometric Proof. Relationships: Perpendicular Lines. The Formal Proof of a Theorem. Perspective on History: The Development of Geometry. Perspective on Application: Patterns. 2. PARALLEL LINES. The Parallel Postulate and Special Angles. Indirect Proof. Proving Lines Parallel. The Angles of a Triangle. Convex Polygons. Symmetry and Transformations. Perspective on History: Sketch of Euclid. Perspective on Application: Non-Euclidean Geometries. 3. TRIANGLES. Congruent Triangles. Corresponding Parts of Congruent Triangles. Isosceles Triangles. Basic Constructions Justified. Inequalities in a Triangle. Perspective on History: Sketch of Archimedes. Perspective on Application: Pascal's Triangle. 4. QUADRILATERALS. Properties of a Parallelogram. The Parallelogram and Kite. The Rectangle, Square, and Rhombus. The Trapezoid. Perspective on History: Sketch of Thales. Perspective on Application: Square Numbers as Sums. 5. SIMILAR TRIANGLES. Ratios, Rates, and Proportions. Similar Polygons. Proving Triangles Similar. The Pythagorean Theorem. Special Right Triangles. Segments Divided Proportionally. Perspective on History: Ceva's Theorem. Perspective on Application: An Unusual Application of Similar Triangles. 6. CIRCLES. Circles and Related Segments and Angles. More Angle Measures in the Circle. Line and Segment Relationships in the Circle. Some Constructions and Inequalities for the Circle. Perspective on History: Circumference of the Earth. Perspective on Application: Sum of the Interior Angles of a Polygon. 7. LOCUS AND CONCURRENCE. Locus of Points. Concurrence of Lines. More About Regular Polygons. Perspective on History: The Value of Perspective on Application: The Nine-Point Circle. 8. AREAS OF POLYGONS AND CIRCLES. Area and Initial Postulates. Perimeter and Area of Polygons. Regular Polygons and Area. Circumference and Area of a Circle. More Area Relationships in the Circle. Perspective on History: Sketch of Pythagoras. Perspective on Application: Another Look at the Pythagorean Theorem. 9. SURFACES AND SOLIDS. Prisms, Area, and Volume. Pyramids, Area, and Volume. Cylinders and Cones. Polyhedrons and Spheres. Perspective on History: Sketch of Rene Descartes. Perspective on Application: Birds in Flight. 10. ANALYTIC GEOMETRY. The Rectangular Coordinate System. Graphs of Linear Equations and Slope. Preparing to do Analytic Proofs. Analytic Proofs. Equations of Lines. Perspective on History: The Banach-Tarski Paradox. Perspective on Application: The Point-of-Division Formulas. 11. INTRODUCTION TO TRIGONOMETRY. The Sine Ratio and Applications. The Cosine Ratio and Applications. The Tangent Ratio and Other Ratios. Applications with Acute Triangles. Perspective on History: Sketch of Plato. Perspective on Application: Radian Measure of Angles. APPENDICES. Appendix A: Algebra review. Appendix B: Summary of Constructions, Postulates, and Theorems and Corollaries.
Digital Rights
eTextbooks and eChapters can be viewed by using the free reader listed below.
Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.
Download Requirements:Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.
Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.
User Help:
Click Here to access the VitalSource Bookshelf FAQ
Digital Rights Management (DRM) Key
Printing - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."
Expires - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).
Reading Aloud - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."
Sharing - Books that cannot be shared with other computers will show "Not Allowed."
Min. Software Version - This is the minimum software version needed to read this book.
Suitable Devices - Hardware known to be compatible with this book. Note: Reader software still needs to be installed.