Geometry

by Jacobs, Harold R.

• ISBN13: 9780716717454
• ISBN10: 071671745X
• Edition: 2nd
• Format: Hardcover
• Copyright: 1987-01-01
• Publisher: W H Freeman & Co

Table of Contents

A Letter to the Student	xi	(2)
Acknowledgments	xiii
Introduction: Euclid, the Surfer, and the Spotter	1	(4)
1 THE NATURE OF DEDUCTIVE REASONING	5	(44)
1. Drawing Conclusions	6	(3)
2. Conditional Statements	9	(5)
3. Equivalent Statements	14	(5)
4. Definitions	19	(4)
5. Valid and Invalid Deductions	23	(5)
6. Direct Proof: Arguments with Two Premises	28	(4)
7. Direct Proof: Arguments with Several Premises	32	(4)
8. Indirect Proof	36	(4)
9. A Deductive System	40	(4)
Summary and Review	44	(3)
Algebra Review	47	(2)
2 POINTS, LINES, AND PLANES	49	(34)
1. Points, Lines, and Planes	50	(6)
2. The Ruler Postulate	56	(4)
3. Properties of Equality	60	(4)
4. Betweenness of Points	64	(5)
5. Line Segments	69	(5)
6. Polygons	74	(5)
Summary and Review	79	(3)
Algebra Review	82	(1)
3 RAYS AND ANGLES	83	(32)
1. Rays and Angles	84	(5)
2. The Protractor Postulate	89	(5)
3. Betweenness of Rays	94	(5)
4. Complementary and Supplementary Angles	99	(6)
5. Linear Pairs and Vertical Angles	105	(5)
6. Parallel and Perpendicular Lines	110	(5)
Summary and Review	115	(3)
Algebra Review	118	(1)
4 CONGRUENT TRIANGLES	119	(48)
1. Triangles	120	(5)
2. Congruent Polygons	125	(5)
3. Proving Triangles Congruent	130	(5)
4. Proving Corresponding Parts Equal	135	(5)
5. The Isosceles Triangle Theorem	140	(5)
6. The S.S.S. Congruence Theorem	145	(5)
7. Constructions	150	(7)
8. More Constructions	157	(5)
Summary and Review	162	(4)
Algebra Review	166	(1)
5 INEQUALITIES	167	(24)
1. Properties of Inequality	168	(5)
2. The Exterior Angle Theorem	173	(5)
3. Triangle Side and Angle Inequalities	178	(5)
4. The Triangle Inequality Theorem	183	(4)
Summary and Review	187	(2)
Algebra Review	189	(2)
6 PARALLEL LINES	191	(44)
1. Proving Lines Parallel	192	(5)
2. Perpendicular Lines	197	(6)
3. The Parallel Postulate	203	(5)
4. Some Consequences of the Parallel Postulate	208	(6)
5. More on Distance	214	(5)
6. The Angles of a Triangle	219	(6)
7. Two More Ways to Prove Triangles Congruent	225	(5)
Summary and Review	230	(4)
Algebra Review	234	(1)
7 QUADRILATERALS	235	(34)
1. Quadrilaterals	236	(5)
2. Parallelograms	241	(5)
3. Quadrilaterals That Are Parallelograms	246	(5)
4. Rectangles, Rhombuses, and Squares	251	(5)
5. Trapezoids	256	(4)
6. The Midsegment Theorem	260	(4)
Summary and Review	264	(3)
Algebra Review	267	(2)
8 TRANSFORMATIONS	269	(38)
1. Reflections	270	(5)
2. Properties of Isometries	275	(6)
3. Translations	281	(5)
4. Rotations	286	(5)
5. Congruence and Isometries	291	(4)
6. Symmetry	295	(4)
Summary and Review	299	(3)
MIDTERM REVIEW	302	(5)
9 AREA	307	(40)
1. Polygonal Regions and Area	308	(4)
2. Squares and Rectangles	312	(5)
3. Triangles	317	(6)
4. Parallelograms and Trapezoids	323	(5)
5. The Pythagorean Theorem	328	(7)
6. Heron's Theorem	335	(7)
Summary and Review	342	(3)
Algebra Review	345	(2)
10 SIMILARITY	347	(42)
1. Ratio and Proportion	348	(5)
2. The Side-Splitter Theorem	353	(7)
3. Similar Polygons	360	(4)
4. The A.A. Similarity Theorem	364	(5)
5. The S.A.S. Similarity Theorem	369	(6)
6. The Angle Bisector Theorem	375	(5)
7. Perimeters and Areas of Similar Polygons	380	(5)
Summary and Review	385	(3)
Algebra Review	388	(1)
11 THE RIGHT TRIANGLE	389	(30)
1. Proportions in a Right Triangle	390	(5)
2. The Pythagorean Theorem Revisited	395	(4)
3. Isosceles and 30(Degree)-60(Degree) Right Triangles	399	(5)
4. The Tangent Ratio	404	(5)
5. The Sine and Cosine Ratios	409	(6)
Summary and Review	415	(4)
12 CIRCLES	419	(42)
1. Circles, Radii, and Chords	420	(6)
2. Tangents	426	(5)
3. Central Angles and Arcs	431	(5)
4. Inscribed Angles	436	(5)
5. Secant Angles	441	(5)
6. Tangent Segments	446	(6)
7. Chord and Secant Segments	452	(5)
Summary and Review	457	(4)
13 THE CONCURRENCE THEOREMS	461	(36)
1. Concyclic Points	462	(5)
2. Cyclic Quadrilaterals	467	(5)
3. Incircles	472	(5)
4. Ceva's Theorem	477	(6)
5. The Centroid of a Triangle	483	(6)
6. Constructions	489	(5)
Summary and Review	494	(3)
14 REGULAR POLYGONS AND THE CIRCLE	497	(38)
1. Regular Polygons	498	(6)
2. The Perimeter of a Regular Polygon	504	(5)
3. The Area of a Regular Polygon	509	(6)
4. Limits	515	(5)
5. The Circumference and Area of a Circle	520	(6)
6. Sectors and Arcs	526	(5)
Summary and Review	531	(4)
15 GEOMETRIC SOLIDS	535	(44)
1. Lines and Planes in Space	536	(5)
2. Rectangular Solids	541	(5)
3. Prisms	546	(4)
4. The Volume of a Prism	550	(5)
5. Pyramids	555	(5)
6. Cylinders and Cones	560	(5)
7. Spheres	565	(6)
8. Similar Solids	571	(5)
Summary and Review	576	(3)
16 NON-EUCLIDEAN GEOMETRIES	579	(26)
1. Geometry on-a Sphere	580	(5)
2. The Saccheri Quadrilateral	585	(6)
3. The Geometries of Lobachevsky and Riemann	591	(5)
4. The Triangle Angle Sum Theorem Revisited	596	(5)
Summary and Review	601	(4)
17 COORDINATE GEOMETRY	605	(36)
1. Coordinate Systems	606	(5)
2. The Distance Formula	611	(4)
3. Slope	615	(4)
4. Parallel and Perpendicular Lines	619	(4)
5. The Midpoint Formula	623	(5)
6. Coordinate Proofs	628	(5)
Summary and Review	633	(2)
FINAL REVIEW	635	(6)
Glossary	641	(6)
Postulates and Theorems	647	(8)
Answers to Selected Exercises	655	(10)
Index	665