Geometry for Enjoyment and Challenge

Name: Geometry for Enjoyment and Challenge
Price: $191.69 USD
Availability: InStock
Author: Richard Rhoad and George Milauskas
ISBN: 9780866099653

by Richard Rhoad and George Milauskas

ISBN13: 9780866099653
ISBN10: 0866099654
Format: Hardcover
Copyright: 1991-06-01
Publisher: HBC

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A Letter to Students

xiv

Introduction to Geometry

(58)

Getting Started

(6)

Measurement of Segments and Angles

(9)

Mathematical Excursion: Geometry in Nature

(1)

Collinearity, Betweenness, and Assumptions

(5)

Beginning Proofs

(5)

Division of Segments and Angles

(8)

Career Profile: The Science of Deduction

(1)

Paragraph Proofs

(3)

Deductive Structure

(5)

Statements of Logic

(5)

Probability

(11)

Chapter Summary

(1)

Review Problems

(6)

Basic Concepts and Proofs

(50)

Perpendicularity

(5)

Complementary and Supplementary Angles

(6)

Drawing Conclusions

(4)

Congruent Supplements and Complements

(6)

Mathematical Excursion: Geometry in Computers

(1)

Addition and Subtraction Properties

(7)

Multiplication and Division Properties

(6)

Career Profile: Studying Bee Communication

(1)

Transitive and Substitution Properties

(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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