Geometry: Student Guide / Edition 5 by E. Warren Moise, Downs | | 9780201253351 | Hardcover | Barnes & Noble
Geometry: Student Guide / Edition 5

Geometry: Student Guide / Edition 5

by E. Warren Moise, Downs
     
 

ISBN-10: 0201253356

ISBN-13: 9780201253351

Pub. Date: 01/01/1991

Publisher: Prentice Hall School Division

Product Details

ISBN-13:
9780201253351
Publisher:
Prentice Hall School Division
Publication date:
01/01/1991
Product dimensions:
6.20(w) x 9.20(h) x 1.30(d)

Table of Contents

Common Sense and Exact Reasoning
1(14)
An organized logical development of geometry
1(5)
Two kinds of problems
6(9)
Euclid
13(2)
Sets, Real Numbers, and Lines
15(34)
Sets
15(5)
Order on the number line
20(7)
Absolute value
27(2)
Rulers and units of distance
29(2)
The Distance Postulate
29(2)
An infinite ruler
31(6)
The Ruler Postulate
33(1)
The Ruler Placement Postulate
34(3)
Betweenness, segments and rays. The Point-Plotting Theorem
37(12)
The Line Postulate
38(6)
Chapter Review
44(3)
David Hilbert
47(2)
Lines, Planes, and Separation
49(28)
Drawing sketches of figures in space
49(3)
Lines, planes, and pictures
52(4)
The Plane-Space Postulate
54(2)
Lines, planes, and pictures (continued)
56(6)
The Flate Plane Postulate
57(1)
The Plane Postulate
58(1)
Intersection of Planes Postulate
59(3)
Convex sets and separation
62(5)
The Plane Separation Postulate
63(2)
The Space Separation Postulate
65(2)
The Seven Bridges of Konigsberg
67(10)
Chapter Review
72(3)
Leonhard Euler
75(2)
Angles and Triangles
77(46)
The basic terms
77(7)
Measuring angles
84(8)
The Angle Measurement Postulate
85(1)
The Angle Construction Postulate
86(1)
The Angle Addition Postulate
86(1)
The Supplement Postulate
87(5)
Some remarks on angles
92(2)
Perpendiculars, right angles and related angles, congruent angles
94(4)
Equivalence relations
98(3)
Some theorems about angles
101(4)
Vertical angles
105(3)
Theorems in the form of hypothesis and conclusion
108(2)
Writing up proofs
110(13)
Chapter Review
117(4)
George David Birkhoff
121(2)
Congruence
123(54)
The idea of a congruence
123(6)
Congruences between triangles
129(7)
The congruence postulates for triangles
136(5)
The SAS Postulate
137(1)
The ASA Postulate
137(1)
The SSS Postulate
137(4)
Thinking up your own proofs
141(6)
Using marks on figures
147(5)
Bisectors of angles
152(2)
Isosceles and equilateral triangles
154(5)
Converses
159(2)
Overlapping triangles. Use of figures to convey information
161(6)
Quadrilaterals, medians, and bisectors
167(10)
Chapter Review
173(4)
A Closer Look at Proof
177(34)
How a deductive system works
177(1)
Indirect proofs
178(3)
Theorems on lines and planes
181(6)
Perpendiculars
187(7)
Introducing auxiliary sets into proofs. The use of the word "let"
194(7)
Making theorems of the ASA and SSS Postulates
201(10)
Chapter Review
207(4)
Geometric Inequalities
211(32)
Making reasonable conjectures
211(2)
Inequalities for numbers, segments, and angles
213(4)
The Exterior Angle Theorem
217(4)
Congruence theorems based on the Exterior Angle Theorem
221(4)
Inequalities in a single triangle
225(4)
The distance between a line and a point. The triangle inequality
229(3)
The Hinge Theorem and its converse
232(4)
Altitudes of triangles
236(7)
Chapter Review
239(4)
Perpendicular Lines and Planes in Space
243(18)
The definition of perpendicularity for lines and planes
243(3)
The basic theorem on perpendiculars
246(3)
Existence and uniqueness
249(4)
Perpendicular lines and planes: a summary
253(8)
Chapter Review
257(4)
Parallel Lines in a Plane
261(46)
Conditions which guarantee parallelism
261(8)
Other conditions that guarantee parallelism
269(3)
The Parallel Postulate
272(5)
Triangles
277(4)
Quadrilaterals in a plane
281(7)
Rhombus, rectangle, and square
288(3)
Some theorems on right triangles
291(3)
Transversals to many parallel lines
294(3)
The Median Concurrence Theorem
297(10)
Eratosthenes
300(1)
Chapter Review
300(7)
Parallel Lines and Planes
307(22)
Basic facts about parallel planes
307(6)
Dihedral angles. Perpendicular planes
313(7)
Projections
320(9)
Chapter Review
325(2)
Nikolai Ivanovitch Lobachevsky
327(2)
Polygonal Regions and Their Areas
329(32)
Polygonal regions
329(8)
The Area Postulate
331(1)
The Congruence Postulate
331(1)
The Area Addition Postulate
332(1)
The Unit Postulate
332(5)
Areas of triangles and quadrilaterals
337(8)
The Pythagorean Theorem
345(6)
Pythagoras
346(5)
Special triangles
351(10)
Chapter Review
356(5)
Similarity
361(42)
The idea of a similarity. Proportionality
361(7)
Similarities between triangles
368(5)
The Basic Proportionality Theorem and its converse
373(7)
The basic similarity theorems
380(11)
Similarities in right triangles
391(3)
Areas of similar triangles
394(9)
Chapter Review
399(4)
Plane Coordinate Geometry
403(46)
Introduction
403(1)
Coordinate systems in a plane
403(6)
Rene Descartes
408(1)
How to draw pictures of coordinate systems on graph paper
409(4)
The slope of a nonvertical line
413(6)
Parallel and perpendicular lines
419(4)
The distance formula
423(4)
The midpoint formula. The point dividing a segment in a given ratio
427(5)
The use of coordinate systems in proving geometric theorems
432(4)
The graph of a condition
436(4)
How to describe a line by an equation
440(9)
Chapter Review
447(2)
Circles and Spheres
449(52)
Basic definitions
449(4)
Tangent lines to circles
453(9)
Tangent planes
462(5)
Arcs of circles
467(4)
Inscribed angles and intercepted arcs
471(5)
Congruent arcs
476(5)
The power theorems
481(7)
Circles in a coordinate plane
488(13)
Chapter Review
495(6)
Characterizations and Constructions
501(34)
Characterizations
501(4)
The use of characterizations in coordinate geometry
505(2)
Concurrence theorems
507(3)
The angle bisectors of a triangle
510(4)
The median concurrence theorem
514(2)
Constructions with straightedge and compass
516(2)
Elementary constructions
518(3)
Elementary constructions (continued)
521(4)
Inscribed and circumscribed circles
525(3)
The impossible construction problems of antiquity
528(7)
Chapter Review
532(3)
Areas of Circles and Sectors
535(22)
Polygons
535(4)
Regular polygons
539(3)
The circumference of a circle. The number π
542(3)
The area of a circle
545(4)
Lengths of arcs and areas of sectors
549(8)
Chapter Review
554(3)
Trigonometry
557(38)
The trigonometric ratios
557(5)
Numerical trigonometry
562(6)
Relations among the trigonometric ratios
568(2)
Radian measure for angles and arcs
570(3)
Directed angles and the winding function
573(4)
Trigonometric functions of angles and of numbers
577(6)
Some basic trigonometric identities
583(3)
More identities. The addition formulas
586(9)
Chapter Review
592(3)
Symmetry, Transformations, and Vectors
595(30)
Introduction
595(1)
Reflections and Symmetric figures
596(5)
Rigid motions: reflections and translations
601(6)
Rotations
607(4)
Vectors
611(5)
A second look at congruence and similarity
616(9)
Chapter Review
621(4)
Solids and Their Volumes
625(31)
Prisms
625(6)
Pyramids
631(5)
Volumes of prisms and pyramids. Cavalieri's Principle
636(9)
The Unit Postulate
637(1)
Cavalieri's Principle
638(6)
Archimedes
644(1)
Cylinders and cones
645(4)
The volume and the surface area of a sphere
649(7)
Chapter Review
654(2)
Postulates and Theorems 656(12)
List of Symbols 668(2)
Index 670(7)
Selected Answers 677

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