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University of Chicago School Mathematics Project : Geometry,9780673459565

University of Chicago School Mathematics Project : Geometry

by
Edition:
2nd
ISBN13:

9780673459565

ISBN10:
067345956X
Format:
Hardcover
Pub. Date:
1/1/1998
Publisher(s):
PRENTICE HALL SCHOOL GROUP
List Price: $83.05

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Table of Contents

Acknowledgments ii
The University of Chicago School mathematics Project iv
Table of Contents
vi
To the Student 1(3)
Points and Lines
4(60)
Dots as Points
6(5)
Locations as Points
11(6)
Ordered Pairs as Points
17(5)
Points in Networks
22(8)
In-Class Activity: Drawing a Box in Perspective
29(1)
Drawing in Perspective
30(5)
The Need for Undefined Terms
35(6)
Postulates for Euclidean Geometry
41(5)
Betweenness and Distance
46(18)
Projects
52(2)
Summary and Vocabulary
54(2)
Progress Self-Test
56(2)
Chapter Review
58(6)
The Language and Logic of Geometry
64(58)
The Need for Definitions
64(5)
``If-Then'' Statements
69(7)
Converses
76(5)
Good Definitions
81(6)
Unions and Intersections of Figures
87(8)
In-class Activity: Defining Polygons
94(1)
Polygons
95(6)
Using an Automatic Drawer: The Triangle Inequality
101(6)
Conjectures
107(15)
Projects
113(2)
Summary and Vocabulary
115(1)
Progress Self-Test
116(2)
Chapter Review
118(3)
Refresher
121(1)
Angles and Lines
122(60)
Angles and Their Measures
124(8)
In-class Activity: Rotating a Triangle
131(1)
Arcs and Rotations
132(5)
Properties of Angles
137(7)
Algebra Properties Used in Geometry
144(6)
One-Step Proof Arguments
150(5)
Parallel Lines
155(6)
Perpendicular Lines
161(6)
Drawing parallel and Perpendicular Lines
167(15)
Projects
172(2)
Summary and Vocabulary
174(2)
Progress Self-Test
176(2)
Chapter Review
178(4)
From Reflections To Congruence
182(60)
Reflecting Points
184(7)
In-class Activity: Reflecting Polygons
190(1)
Reflecting Figures
191(6)
Miniature Golf and Billiards
197(6)
Composing Reflections over Parallel Lines
203(7)
Composing Reflections over Intersecting Lines
210(6)
Translations and Vectors
216(6)
Isometries
222(6)
When are Figures Congruent?
228(14)
Projects
233(2)
Summary and Vocabulary
235(1)
Progress Self-Test
236(2)
Chapter Review
238(4)
Proofs Using Congruence
242(56)
Corresponding Parts of Congruent Figures
244(6)
Congruence and Equality
250(6)
One-Step Congruence Proofs
256(7)
In-class Activity: Circle Constructions
262(1)
Proofs Using Transitivity
263(7)
In-class Activity: Investigating Perpendicular Bisectors
269(1)
Proofs Using Reflections
270(6)
Auxiliary Figures and Uniqueness
276(5)
Sums of Angle Measures in Polygons
281(17)
Projects
288(2)
Summary and Vocabulary
290(1)
Progress Self-Test
291(1)
Chapter Review
292(6)
Polygons and Symmetry
298(64)
Reflection-symmetric Figures
300(9)
In-class Activity: Angle Bisectors, Medians, ⊥Bisectors of a Triangle
308(1)
Isosceles Triangles
309(7)
Types of Quadrilaterals
316(7)
In-class Activity: Conjectures about Quadrilaterals
322(1)
Properties of Kites
323(6)
Properties of Trapezoids
329(6)
Rotation Symmetry
335(6)
In-class Activity: Symmetry Lines in Polygons
340(1)
Regular Polygons
341(6)
Regular Polygons and Schedules
347(15)
Projects
352(2)
Summary and Vocabulary
354(2)
Progress Self-Test
356(2)
Chapter Review
358(4)
Triangle Congruence
362(72)
Drawing Triangles
364(6)
Triangle Congruence Theorems
370(8)
Proofs Using Triangle Congruence Theorems
378(6)
Overlapping Triangles
384(5)
The SSA Condition and HL Congruence
389(8)
Tessellations
397(8)
In-class Activity: Congruent Parts of Parallelograms
404(1)
Properties of Parallelograms
405(6)
Sufficient conditions for Parallelograms
411(5)
Exterior Angles
416(18)
Projects
423(2)
Summary and Vocabulary
425(1)
Progress self-Test
426(2)
Chapter Review
428(5)
Refresher
433(1)
Perimeters And Areas
434(60)
Perimeter Formulas
436(5)
Fundamental Properties of Area
441(6)
Areas of irregular Regions
447(6)
Areas of Triangles
453(6)
Areas of Trapezoids
459(7)
In-class Activity: Creating Squares from Right Triangles
465(1)
The Phythagorean Theorem
466(8)
In-class Activity: Estimating the Circumference of a Circle
473(1)
Arc Length and circumference
474(6)
In-class Activity: Estimating the Area of a circle
479(1)
The Area of a circle
480(14)
Projects
485(2)
Summary and vocabulary
487(1)
Progress Self-Test
488(2)
Chapter Review
490(4)
Three-Dimensional Figures
494(68)
Points, Lines, and Planes in Space
496(4)
Parallel and Perpendicular Lines
500(5)
Prisms and Cylinders
505(6)
Pyramids and cones
511(6)
Spheres and Sections
517(8)
Reflection Symmetry in Space
525(6)
Viewing Solids and surfaces
531(6)
In-class Activity: Building Cubes
536(1)
Making Surfaces
537(7)
In-class Activity: Coloring Map
543(1)
Maps and the Four-Color Theorem
544(18)
Projects
552(2)
Summary and Vocabulary
554(2)
Progress Self-Test
556(2)
Chapter Review
558(4)
Surface Areas And Volumes
562(58)
Surface Areas of Prisms and Cylinders
564(6)
In-class Activity: Lateral Area of Regular Pyramids
569(1)
Surface Area of Pyramids and Cones
570(6)
Fundamental Properties of Volume
576(6)
Multiplication, Area, and Volume
582(5)
Volumes of Prisms and Cylinders
587(6)
Organizing Formulas
593(6)
In-class Activity: Building a Prism from Pyramids
598(1)
Volumes of Pyramids and Cones
599(5)
The Volume of a Sphere
604(5)
The Surface Area of a Sphere
609(11)
Projects
613(2)
Summary and Vocabulary
615(1)
Progress Self-Test
616(1)
Chapter Review
617(3)
Indirect and Coordinate Proofs
620(64)
The Logic of Making Conclusions
622(6)
Negations
628(6)
Ruling Out Possibilities
634(5)
Indirect Proof
639(6)
Proofs with Coordinates
645(6)
The Distance Formula
651(5)
Equations for Circles
656(6)
In-class Activity: Connecting Midpoints in a Triangle
661(1)
Means and Midpoints
662(6)
Three-Dimensional Coordinates
668(16)
Projects
675(2)
Summary and Vocabulary
677(2)
Progress Self-Test
679(1)
Chapter Review
680(4)
Similarity
684(52)
The Transformation Sk
686(6)
In-class Activity: Drawing Size-Change Images
691(1)
Size-Changes
692(6)
Properties of Size Changes
698(7)
Proportions
705(6)
Similar Figures
711(6)
The Fundamental Theorem of Similarity
717(7)
Can There Be Giants
724(12)
Projects
729(2)
Summary and Vocabulary
731(1)
Progress Self-Test
732(1)
Chapter Review
733(3)
Similar Triangles and Trigonometry
736(62)
The SSA Similarity Theorem
738(6)
The AA and SAS Similarity Theorem
744(7)
The Side-Splitting Theorem
751(8)
In-class Activity: Similarity in Right Triangles
758(1)
Geometric Means in Right Triangles
759(6)
Special Right Triangles
765(7)
In-class Activity: Ratios of Legs in Right Triangles
771(1)
The Tangent of an Angle
772(5)
The Sine and Cosine Ratios
777(7)
More Work with Vectors and Area
784(14)
Projects
789(2)
Summary and Vocabulary
791(1)
Progress Self-Test
792(2)
Chapter Review
794(4)
Further Work With Circles
798(64)
Chord Length and Arc Measure
800(6)
The Inscribed Angle Theorem
806(7)
Locating the Center of a Circle
813(5)
Angles Formed by Chords or Secants
818(5)
Tangents to Circles and Spheres
823(6)
Angles Formed by Tangents
829(7)
In-class Activity: Investigating Lengths of Chords. Secants, and Tangents
835(1)
Lengths of Chords, Secants, and Tangents
836(6)
The Isoperimetric Inequality
842(6)
The Isoperimetric Inequality in three Dimensions
848(14)
Projects
853(2)
Summary and Vocabulary
855(1)
Progress Self-Test
856(2)
Chapter Review
858(4)
Appendix A: Theorems 862(6)
Appendix B: Postulates 868(2)
Appendix C: Formulas 870(2)
Selected Answers 872(35)
Glossary 907(9)
Index 916(11)
List of Symbols 927(1)
Photo Acknowledgments 928


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