Geometry for Enjoyment and Challenge,9780866099653

Geometry for Enjoyment and Challenge

by
ISBN13: 9780866099653
ISBN10: 0866099654
Format: Hardcover
Pub. Date: 1991-06-01
Publisher(s): HBC
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Table of Contents

A Letter to Students xiv
Introduction to Geometry
2(58)
Getting Started
3(6)
Measurement of Segments and Angles
9(9)
Mathematical Excursion: Geometry in Nature
17(1)
Collinearity, Betweenness, and Assumptions
18(5)
Beginning Proofs
23(5)
Division of Segments and Angles
28(8)
Career Profile: The Science of Deduction
35(1)
Paragraph Proofs
36(3)
Deductive Structure
39(5)
Statements of Logic
44(5)
Probability
49(11)
Chapter Summary
53(1)
Review Problems
54(6)
Basic Concepts and Proofs
60(50)
Perpendicularity
61(5)
Complementary and Supplementary Angles
66(6)
Drawing Conclusions
72(4)
Congruent Supplements and Complements
76(6)
Mathematical Excursion: Geometry in Computers
81(1)
Addition and Subtraction Properties
82(7)
Multiplication and Division Properties
89(6)
Career Profile: Studying Bee Communication
94(1)
Transitive and Substitution Properties
95(5)
Vertical Angles
100(10)
Chapter Summary
104(1)
Review Problems
105(5)
Congruent Triangles
110(58)
What Are Congruent Figures?
111(4)
Three Ways to Prove Triangles Congruent
115(10)
CPCTC and Circles
125(6)
Mathematical Excursion: Structural Congruent Triangles
130(1)
Beyond CPCTC
131(7)
Career Profile: Symmetry Unlocks Culture
137(1)
Overlapping Triangles
138(4)
Types of Triangles
142(6)
Angle-Side Theorems
148(8)
The HL Postulate
156(12)
Chapter Summary
161(1)
Review Problems
162(3)
Cumulative Review, Chapters 1-3
165(3)
Lines in the Plane
168(42)
Detours and Midpoints
169(7)
The Case of the Missing Diagram
176(4)
A Right-Angle Theorem
180(4)
The Equidistance Theorems
184(8)
Career Profile: Plotting the Structure of a Molecule
191(1)
Introduction to Parallel Lines
192(6)
Historical Snaphshot: From Mud to the Stars
197(1)
Slope
198(12)
Chapter Summary
205(1)
Review Problems
206(4)
Parallel Lines and Related Figures
210(58)
Indirect Proof
211(5)
Career Profile: A Line to the Stars
215(1)
Proving That Lines Are Parallel
216(8)
Congruent Angles Associated with Parallel Lines
224(10)
Four-Sided Polygons
234(7)
Historical Snapshot: A New Kid of Proof
240(1)
Properties of Quadrilaterals
241(8)
Proving That a Quadrilateral Is a Parallelogram
249(6)
Proving That Figures Are Special Quadrilaterals
255(13)
Chapter Summary
263(1)
Review Problems
264(4)
Lines and Planes in Space
268(26)
Relating Lines to Planes
269(7)
Career Profile: The Geometry of Architecture
275(1)
Perpendicularity of a Line and a Plane
276(6)
Historical Snapshot: Probability and Pi
281(1)
Basic Facts About Parallel Planes
282(12)
Chapter Summary
287(1)
Review Problems
288(3)
Cumulative Review, Chapters 1-6
291(3)
Polygons
294(30)
Triangle Application Theorems
295(7)
Two Proof-Oriented Triangle Theorems
302(5)
Formulas Involving Polygons
307(7)
Career Profile: Precise Angles Pay Off
313(1)
Regular Polygons
314(10)
Mathematical Excursion: Polygons in the North Country
318(1)
Chapter Summary
319(1)
Review Problems
320(4)
Similar Polygons
324(42)
Ratio and Proportion
325(7)
Similarity
332(7)
Methods of Proving Triangles Similar
339(6)
Congruence and proportions in Similar Triangles
345(6)
Three Theorems Involving Proportions
351(15)
Career Profile: Putting Quilts in Perspective
359(1)
Chapter Summary
360(1)
Review Problems
361(4)
Historical Snapshot: A Master Technologist
365(1)
The Pythagorean Theorem
366(72)
Review of Radicals and Quadratic Equations
367(3)
Introduction to Circles
370(7)
Altitude-on-Hypotenuse Theorems
377(7)
Mathematical Excursion: The Pythagorean Theorem and Trigonometric Ratios
383(1)
Geometry's Most Elegant Theorem
384(8)
The Distance Formula
392(6)
Career Profile: Finding Distances with Lasers
397(1)
Families of Right Triangles
398(7)
Special Right Triangles
405(8)
The Pythagorean Theorem and Space Figures
413(5)
Introduction to Trigonometry
418(5)
Trigonometric Ratios
423(15)
Chapter Summary
428(1)
Review Problems
429(5)
Cumulative Review, Chapters 1-9
434(4)
Circles
438(72)
The Circle
439(7)
Congruent Chords
446(4)
Arcs of a Circle
450(9)
Secants and Tangents
459(9)
Angles Related to a Circle
468(11)
More Angle-Arc Theorems
479(7)
Inscribed and Circumscribed Polygons
486(7)
Mathematical Excursion: Tangent, Slope, and Loops
492(1)
The Power Theorems
493(6)
Career Profile: From Asteroids to Dust
498(1)
Circumference and Arc Length
499(11)
Chapter Summary
504(1)
Review Problems
505(5)
Area
510(50)
Understanding Area
511(5)
Areas of Parallelograms and Triangles
516(7)
The Area of a Trapezoid
523(5)
Areas of Kites and Related Figures
528(3)
Areas of Regular Polygons
531(6)
Mathematical Excursion: Tiling and Area
536(1)
Areas of Circles, Sectors, and Segments
537(6)
Career Profile: Geometry in Visual Communication
542(1)
Ratios of Areas
543(7)
Hero's and Brahmagupta's Formulas
550(10)
Chapter Summary
553(1)
Review Problems
554(6)
Surface Area and Volume
560(44)
Surface Areas of Prisms
561(4)
Surface Areas of Pyramids
565(5)
Career Profile: Packaging Ideas
569(1)
Surface Areas of Circular Solids
570(5)
Volumes of Prisms and Cylinders
575(8)
Volumes of Pyramids and Cones
583(6)
Volumes of Spheres
589(15)
Chapter Summary
593(1)
Review Problems
594(4)
Cumulative Review, Chapters 1-12
598(5)
Historical Snapshot: The Shape of the Universe
603(1)
Coordinate Geometry Extended
604(44)
Graphing Equations
605(5)
Equations of Lines
610(8)
Systems of Equations
618(4)
Graphing Inequalities
622(4)
Three-Dimensional Graphing and Reflections
626(7)
Career Profile: Image-Producing Waves
632(1)
Circles
633(5)
Coordinate-Geometry Practice
638(10)
Historical Snapshot: The Serpent and the Peacock
642(1)
Chapter Summary
643(1)
Review Problems
644(4)
Locus and Constructions
648(38)
Locus
649(7)
Historical Snapshot: The Geometry of Music
655(1)
Compound Locus
656(4)
The Concurrence Theorems
660(6)
Basic Constructions
666(7)
Applications of the Basic Constructions
673(5)
Triangle Constructions
678(8)
Chapter Summary
682(1)
Review Problems
683(2)
Career Profile: Darkness Visible
685(1)
Inequalities
686(26)
Number Properties
687(4)
Career Profile: Deductions from Seismic Waves
690(1)
Inequalities in a Triangle
691(6)
The Hinge Theorems
697(15)
Mathematical Excursion: Inequalities
701(1)
Chapter Summary
702(1)
Review Problems
703(3)
Cumulative Review, Chapters 1-15
706(6)
Enrichment Topics
712(28)
The Point-Line Distance Formula
713(4)
Career Profile: Planetary Portraits
716(1)
Two Other Useful Formulas
717(4)
Stewart's Theorem
721(3)
Ptolemy's Theorem
724(4)
Historical Snapshot: Dynamic Geometry
727(1)
Mass Points
728(3)
Inradius and Circumradius Formulas
731(3)
Formulas for You to Develop
734(6)
Chapter Summary
737(1)
Review Problems
738(2)
List of Postulates and Theorems 740(10)
Selected Answers 750(8)
Glossary 758(5)
Index 763(7)
Symbols Used in Geometry 770

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