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: Perpindicular Lines 1.7 The Formal Proof of a
Theorem PERSPECTIVE ON HISTORY: The Development of Geometry
PERSPECTIVE ON APPLICATION: Patterns Summary Review Exercises
Chapter Test
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 PERSPECTIVE ON HISTORY:
Sketch of Euclid PERSPECTIVE ON APPLICATION: Non-Euclidean
Geometries Summary Review Exercises Chapter Test
Chapter 3 Triangles
3.1 Congruent Triangles 3.2 Correspondening Parts of Congruent
Triangles 3.3 Isosceles Triangles 3.4 Basic Constructions Justified
3.5 Inequalities in a Triangle PERSPECTIVE ON HISTORY: Sketch of
Archimedes PERSPECTIVE ON APPLICATION: Pascal's Triangle Summary
Review Exercises Chapter Test
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
PERSPECTIVE ON HISTORY: Sketch of Thales PERSPECTIVE ON
APPLICATION: Square Numbers as Sums Summary Review Exercises
Chapter Test
Chapter 5 Similar Triangles
5.1 Ratios, Rates and Proportions 5.2 Similar Polygons 5.3 Proving
Triangles Similar 5.4 The Pythagorean Theory 5.5 Special Right
Triangles 5.6 Segments Divided Proportionally PERSPECTIVE ON
HISTORY: Ceva's Proof PERSPECTIVE ON APPLICATION: An Unusual
Application of Similar Triangles Summary Review Exercises Chapter
Test
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 Construction and Inequalities in the Circle PERSPECTIVE ON
HISTORY: Circumference of the Earth PERSPECTIVE ON APPLICATION: Sum
of the Interior Angles of a Polygon Summary Review Exercises
Chapter Test
Chapter 7 Locus and Concurrence
7.1 Locus of Points 7.2 Concurrence of Lines 7.3 More About Regular
Polygons PERSPECTIVE ON HISTORY: The Value of p (Pi) PERSPECTIVE ON
APPLICATION: The Nine-Point Circle Summary Review Exercises Chapter
Test
Chapter 8 Areas of Polygons and Circles
8.1 Areas 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 PERSPECTIVE ON
HISTORY: Sketch of Pythagoras PERSPECTIVE ON APPLICATION: Another
Look at the Pythagorean Theorem Summary Review Exercises Chapter
Test
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 PERSPECTIVE ON
HISTORY: Sketch of René Descartes PERSPECTIVE ON APPLICATION: Birds
in Flight Summary Review Exercises Chapter Test
Chapter 10 Analytical 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 10.6 A Three-Dimensional
Coordinate System PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox
PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas Summary
Review Exercises Chapter Test
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 PERSPECTIVE ON HISTORY: Sketch of
Plato PERSPECTIVE ON APPLICATION: Radian Measure of Angles Summary
Review Exercises Chapter Test
Appendix A: Algebra Review
Appendix B: Summaries of Constructions, Postulates, Theorems, and
Corollaries
Answers
Glossary
Index
Daniel C. Alexander is professor emeritus of mathematics at Parkland College in Champaign, Illinois. Before retiring, Professor Alexander taught mathematics at the secondary and college levels for over 40 years. He was a member and officer of IMACC, a member of AMATYC, and remains a member of ICTM. In addition to presenting and participating in panel discussions at these conferences, Professor Alexander has published numerous articles in the ICTM, NCTM and AMATYC mathematics journals. Professor Alexander holds undergraduate and graduate degrees from Southern Illinois University, and completed considerable post-graduate course work as well. Before her retirement, Geralyn M. Koeberlein taught mathematics at Mahomet-Seymour High School in Mahomet, Illinois, for 34 years. She taught several levels of math, from Algebra I to AB Calculus, and spent the last few years of her career as chair of the Math and Science Department. After receiving her Master's Degree from the University of Illinois early in her teaching years, Geralyn continued her education by receiving over 90 hours of post-graduate credit. She is a former member of the ICTM and the NCTM.
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: Perpindicular Lines 1.7 The Formal Proof of a Theorem PERSPECTIVE ON HISTORY: The Development of Geometry PERSPECTIVE ON APPLICATION: Patterns Summary Review Exercises Chapter Test 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 PERSPECTIVE ON HISTORY: Sketch of Euclid PERSPECTIVE ON APPLICATION: Non-Euclidean Geometries Summary Review Exercises Chapter Test Chapter 3 Triangles 3.1 Congruent Triangles 3.2 Correspondening Parts of Congruent Triangles 3.3 Isosceles Triangles 3.4 Basic Constructions Justified 3.5 Inequalities in a Triangle PERSPECTIVE ON HISTORY: Sketch of Archimedes PERSPECTIVE ON APPLICATION: Pascal's Triangle Summary Review Exercises Chapter Test 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 PERSPECTIVE ON HISTORY: Sketch of Thales PERSPECTIVE ON APPLICATION: Square Numbers as Sums Summary Review Exercises Chapter Test Chapter 5 Similar Triangles 5.1 Ratios, Rates and Proportions 5.2 Similar Polygons 5.3 Proving Triangles Similar 5.4 The Pythagorean Theory 5.5 Special Right Triangles 5.6 Segments Divided Proportionally PERSPECTIVE ON HISTORY: Ceva's Proof PERSPECTIVE ON APPLICATION: An Unusual Application of Similar Triangles Summary Review Exercises Chapter Test 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 Construction and Inequalities in the Circle PERSPECTIVE ON HISTORY: Circumference of the Earth PERSPECTIVE ON APPLICATION: Sum of the Interior Angles of a Polygon Summary Review Exercises Chapter Test Chapter 7 Locus and Concurrence 7.1 Locus of Points 7.2 Concurrence of Lines 7.3 More About Regular Polygons PERSPECTIVE ON HISTORY: The Value of p (Pi) PERSPECTIVE ON APPLICATION: The Nine-Point Circle Summary Review Exercises Chapter Test Chapter 8 Areas of Polygons and Circles 8.1 Areas 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 PERSPECTIVE ON HISTORY: Sketch of Pythagoras PERSPECTIVE ON APPLICATION: Another Look at the Pythagorean Theorem Summary Review Exercises Chapter Test 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 PERSPECTIVE ON HISTORY: Sketch of Rene Descartes PERSPECTIVE ON APPLICATION: Birds in Flight Summary Review Exercises Chapter Test Chapter 10 Analytical 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 10.6 A Three-Dimensional Coordinate System PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas Summary Review Exercises Chapter Test 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 PERSPECTIVE ON HISTORY: Sketch of Plato PERSPECTIVE ON APPLICATION: Radian Measure of Angles Summary Review Exercises Chapter Test Appendix A: Algebra Review Appendix B: Summaries of Constructions, Postulates, Theorems, and Corollaries Answers Glossary Index
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