Geometry for Enjoyment and Challenge

by Richard Rhoad and George Milauskas

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

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