Table of Contents - Glencoeglencoe.com/sec/math/ose/geoca/2006/docs/contents.pdf · Table Of Contents. Segment Measure and Coordinate Graphing.....48 Check Your Readiness

Reasoning in Geometry....................................................................................2

Check Your Readiness..........................................................................................31–1 Patterns and Inductive Reasoning.............................................................4

Investigation: To Grandmother’s House We Go! ...............................101–2 Points, Lines, and Planes............................................................................12

Quiz 1: Lessons 1–1 and 1–2 .......................................................................171–3 Postulates..................................................................................................181–4 Conditional Statements and Their Converses........................................24

Quiz 2: Lessons 1– 3 and 1– 4......................................................................281–5 Tools of the Trade.........................................................................................291–6 A Plan for Problem Solving.......................................................................35

ASSESSMENTStudy Guide and Assessment ....................................................................42Chapter Test .....................................................................................................45Preparing for Standardized Tests..................................................................46

• Architect........................................................23• Real Estate Agent.........................................41

• Multiple Choice..........................17, 28, 34, 40• Open Ended..................................................22

......................6• Paper Folding.......................................15, 19, 31

• Research ..............................................................3• Data Update.......................................................9• Career Data................................................23, 41• Review Activities............................................42• Test Practice........................................................47

.....................32

...............................................................16, 34

Standardized Test Practice

viii

Chapter 1

Lesson 1–2, page 12

Table Of Contents

Segment Measure and Coordinate Graphing.....................................48

Check Your Readiness....................................................................................492–1 Real Numbers and Number Lines...........................................................502–2 Segments and Properties of Real Numbers...........................................56

Quiz 1: Lessons 2–1 and 2–2...................................................................612–3 Congruent Segments ...................................................................................622–4 The Coordinate Plane .............................................................................68

Quiz 2: Lessons 2– 3 and 2– 4......................................................................73Investigation: “V” Is for Vector...............................................................74

2–5 Midpoints.......................................................................................................76

ASSESSMENTStudy Guide and Assessment ....................................................................82Chapter Test .....................................................................................................85Preparing for Standardized Tests ..............................................................86

• Multiple Choice ..................................................................55, 61, 67, 73• Open Ended.........................................................................................81

..............................................69, 76• Construction...................................................................................65

• Research................................................................................................49• Data Update.........................................................................................55• Review Activities...........................................................................82• Test Practice ....................................................................................87

............................................................79

..................................................................................................................68


ix

Chapter 2

Lesson 2– 4, page 72

Angles............................................................................................................................88

Check Your Readiness............................................................................893–1 Angles................................................................................................................903–2 Angle Measure.........................................................................................96

Investigation: Those Magical Midpoints.............................................1023–3 The Angle Addition Postulate.............................................................1043–4 Adjacent Angles and Linear Pairs of Angles.........................................110

Quiz 1: Lessons 3 –1 through 3 – 4 ............................................................1143–5 Complementary and Supplementary Angles .....................................1163–6 Congruent Angles......................................................................................122

Quiz 2: Lessons 3 –5 and 3 – 6...................................................................1273–7 Perpendicular Lines..............................................................................128

ASSESSMENTStudy Guide and Assessment ..................................................................134Chapter Test...................................................................................................137Preparing for Standardized Tests .................................................................138

• Astronomer ......................................................95• Drafter..........................................................115

• Multiple Choice.....94, 109, 114, 121, 127, 133• Open Ended................................................101

..................104• Construction................................99, 107, 130

• Research.........................................................89• Career Data..............................................95, 115• Data Update................................................101• Review Activities..........................................134• Test Practice ..............................................139

...................112

.....................110, 111, 113, 116, 127, 128, 136


x

Chapter 3


xi

Chapter 4


Parallels...................................................................................................................140

Check Your Readiness ...................................................................................1414–1 Parallel Lines and Planes...........................................................................1424–2 Parallel Lines and Transversals...........................................................148

Investigation: When Does a Circle Become a Line? ..........................1544–3 Transversals and Corresponding Angles.............................................156

Quiz 1: Lessons 4 –1 through 4 – 3 .....................................................1614–4 Proving Lines Parallel...............................................................................1624–5 Slope........................................................................................................168

Quiz 2: Lessons 4 – 4 and 4 –5 ............................................................1734–6 Equations of Lines.................................................................................174

ASSESSMENTStudy Guide and Assessment ..................................................................180Chapter Test...................................................................................................183Preparing for Standardized Tests ............................................................184

• Multiple Choice............................................147, 161, 167, 173, 179• Open Ended..................................................................................153

.............................................149, 169• Construction ......................................................................................162

• Research.........................................................................................141• Data Update..................................................................................178• Review Activities..............................................................................180• Test Practice .......................................................................................185

.......................................................170

.......................................142, 148, 153, 156, 159, 163, 171, 172, 173


xii

Triangles and Congruence ..................................................................186

Check Your Readiness..........................................................................1875–1 Classifying Triangles...................................................................................1885–2 Angles of a Triangle..............................................................................1935–3 Geometry in Motion..................................................................................198

Quiz 1: Lessons 5 –1 through 5 – 3...........................................................2025– 4 Congruent Triangles..................................................................................203

Investigation: Take a Shortcut...............................................................2085–5 SSS and SAS .......................................................................................210

Quiz 2: Lessons 5 – 4 and 5 –5 ....................................................................2145–6 ASA and AAS..............................................................................................215


• Multiple Choice..........192, 202, 207, 214, 219• Open Ended................................................197

..................203• Construction .............................................210

• Research.......................................................187• Data Update................................................191• Review Activities..........................................220• Test Practice ...................................................225

.................193

...........................................191, 192, 197, 213

..........................188, 189, 199, 211, 215, 216


Chapter 5


xiii

More About Triangles ...............................................................................226

Check Your Readiness.............................................................................2276–1 Medians ........................................................................................................2286–2 Altitudes and Perpendicular Bisectors.................................................2346–3 Angle Bisectors of Triangles....................................................................240

Quiz 1: Lessons 6 –1 through 6 – 3...........................................................243Investigation: What a Circle! ..............................................................244

6–4 Isosceles Triangles......................................................................................2466–5 Right Triangles............................................................................................2516–6 The Pythagorean Theorem........................................................................2566–7 Distance on the Coordinate Plane....................................................262

ASSESSMENTQuiz 2: Lessons 6 – 4 through 6 –7.....................................................267Study Guide and Assessment ..................................................................268Chapter Test...................................................................................................271Preparing for Standardized Tests............................................................272

• Multiple Choice ..............................233, 239, 243,255, 261, 267

• Open Ended........................................................250

.......................262• Construction..........................................228, 234

• Research...............................................................227• Data Update ..................................................255• Review Activities ..........................................268• Test Practice ........................................................273

......................246

.................237, 238, 240, 243, 251, 254, 261, 270

....................................................................236, 256


Chapter 6

Lesson 6 – 3, page 243

Triangle Inequalities ......................................................................................274

Check Your Readiness..........................................................................2757–1 Segments, Angles, and Inequalities.......................................................2767–2 Exterior Angle Theorem.......................................................................282

Investigation: Linguine Triangles—Hold the Sauce! ........................2887–3 Inequalities Within a Triangle.................................................................290

Quiz: Lessons 7–1 through 7– 3............................................................2957–4 Triangle Inequality Theorem...............................................................296


• Pilot..................................................................301

• Multiple Choice..........................281, 287, 300• Open Ended................................................295

.................283

• Research.......................................................275• Data Update................................................277• Career Data ....................................................301• Review Activities..........................................302• Test Practice ...................................................307

..................290

..............279, 281, 282, 286, 290, 294, 298, 299


xiv

Chapter 7


xv

Quadrilaterals ....................................................................................................308

Check Your Readiness..................................................................................3098–1 Quadrilaterals........................................................................................3108–2 Parallelograms.......................................................................................316

Quiz 1: Lessons 8–1 and 8–2....................................................................3218–3 Tests for Parallelograms....................................................................3228–4 Rectangles, Rhombi, and Squares.......................................................327

Quiz 2: Lessons 8–3 and 8–4................................................................3328–5 Trapezoids....................................................................................................333

ASSESSMENTInvestigation: Go Fly a Kite! .....................................................................340Study Guide and Assessment ..................................................................342Chapter Test...................................................................................................345Preparing for Standardized Tests............................................................346

• Designer................................................................339

• Multiple Choice ........................315, 321, 332, 338• Open Ended........................................................326

.....312, 322, 328

• Research...............................................................309• Data Update ..................................................332• Career Data.........................................................339• Review Activities............................................342• Test Practice ........................................................347

......................316

...................................310, 320, 321, 328, 337, 338

..............................................................311, 316, 327


Chapter 8


Proportions and Similarity.....................................................................348

Check Your Readiness .............................................................................3499–1 Using Ratios and Proportions .............................................................3509–2 Similar Polygons................................................................................356

Quiz 1: Lessons 9–1 and 9–2.................................................................3619–3 Similar Triangles....................................................................................3629–4 Proportional Parts and Triangles........................................................3689–5 Triangles and Parallel Lines..............................................................374

Investigation: Are Golden Triangles Expensive? ...............................3809–6 Proportional Parts and Parallel Lines...................................................382

Quiz 2: Lessons 9–3 through 9–6.........................................................3879–7 Perimeters and Similarity..........................................................................388


• Carpenter............................................................................................379

• Multiple Choice ..............................................361, 367, 373, 378, 393• Open Ended.......................................................................355, 387

..........................362, 370, 382, 388

• Research..........................................................349• Data Update....................................................354• Career Data.................................................379• Review Activities .......................................394• Test Practice ................................................399

...................371

..........355, 362, 368, 380, 381, 382, 393


xvi

Chapter 9


xvii

Polygons and Area.....................................................................................400

Check Your Readiness..................................................................................40110 –1 Naming Polygons ..........................................................................................40210 – 2 Diagonals and Angle Measure............................................................40810 – 3 Areas of Polygons..........................................................................................413

Quiz 1: Lessons 10–1 through 10–3.....................................................41810 – 4 Areas of Triangles and Trapezoids ........................................................41910 – 5 Areas of Regular Polygons ......................................................................425

Investigation: How About That Pythagoras! ....................................43210 – 6 Symmetry.....................................................................................................434

Quiz 2: Lessons 10–4 through 10–6.....................................................43910 –7 Tessellations.................................................................................................440


• HVAC Technician.............................................................................431• Graphic Artist...............................................................................445

• Multiple Choice...................................407, 412, 418, 430, 439, 444• Open Ended.......................................................................................424

................................408, 415, 420• Construction.................................................................................425

• Research..............................................................................................401• Data Update ..............................................................................414• Career Data........................................................................431, 445• Review Activities.........................................................................446• Test Practice ..................................................................................451

...................................................427

.............................403, 408, 411, 413, 419, 421, 425, 426, 430, 440

...........................................................................................................402


Chapter 10

A

F

ED

C

B


Circles ..............................................................................................................452

Check Your Readiness..................................................................................45311–1 Parts of a Circle..................................................................................454

Investigation: A Locus Is Not a Grasshopper! .................................46011–2 Arcs and Central Angles ......................................................................462

Quiz 1: Lessons 11–1 and 11–2...........................................................46711–3 Arcs and Chords....................................................................................46811–4 Inscribed Polygons................................................................................47411–5 Circumference of a Circle.........................................................................478

Quiz 2: Lessons 11–3 through 11–5......................................................48211–6 Area of a Circle......................................................................................483


• Woodworker...............................................459

• Multiple Choice...........458, 473, 477, 482, 487• Open Ended................................................467

• Paper Folding................................................469• Construction ...............................................474

• Research..........................................................453• Career Data.................................................459• Data Update....................................................479• Review Activities .......................................488• Test Practice ................................................493

...................478

...................................454, 462, 468, 476, 478


xviii

Chapter 11


Surface Area and Volume...........................................................................494

Check Your Readiness..................................................................................49512–1 Solid Figures................................................................................................496

Investigation: Take a Slice......................................................................50212–2 Surface Areas of Prisms and Cylinders.................................................50412–3 Volumes of Prisms and Cylinders ......................................................510

Quiz 1: Lessons 12–1 through 12–3..........................................................51512–4 Surface Areas of Pyramids and Cones...............................................51612–5 Volumes of Pyramids and Cones...........................................................522

Quiz 2: Lessons 12–4 and 12–5.............................................................52712–6 Spheres....................................................................................................52812–7 Similarity of Solid Figures .......................................................................534


• Multiple Choice......................................501, 509, 515, 521, 533, 539• Open Ended.......................................................................................527

..........................................510, 522

• Research..........................................................495• Data Update..............................................530• Review Activities ...........................................540• Test Practice ...................................................545

....................506

...................................................................511

....................496, 497, 504, 506, 516, 528, 529


xix

Chapter 12


Right Triangles and Trigonometry......................................................546

Check Your Readiness..................................................................................54713–1 Simplifying Square Roots ..........................................................................54813–2 45°-45°-90° Triangles..........................................................................554

Quiz 1: Lessons 13–1 and 13–2.............................................................55813–3 30°-60°-90° Triangles..........................................................................55913–4 Tangent Ratio.........................................................................................564

Quiz 2: Lessons 13–3 and 13–4 ............................................................569Investigation: I Spy......................................................................................570

13–5 Sine and Cosine Ratios.........................................................................572


• Multiple Choice.......................................................553, 563, 569, 577• Open Ended.......................................................................................558

..........................................554, 559

• Research..............................................................................................547• Data Update .................................................................................561• Review Activities.........................................................................578• Test Practice ..................................................................................583

...................................................574

.............................................................561, 562, 564, 566, 569, 572


xx

Chapter 13


xxi

Chapter 14


Circle Relationships ..................................................................................584

Check Your Readiness .............................................................................58514–1 Inscribed Angles....................................................................................58614–2 Tangents to a Circle...............................................................................592

Investigation: The Ins and Outs of Polygons....................................59814– 3 Secant Angles.........................................................................................600

Quiz 1: Lessons 14–1 through 14–3...................................................60514– 4 Secant-Tangent Angles..............................................................................60614– 5 Segment Measures .....................................................................................612

Quiz 2: Lessons 14–4 and 14–5............................................................... 61714– 6 Equations of Circles...................................................................................618

ASSESSMENTStudy Guide and Assessment ..................................................................624Chapter Test...................................................................................................627Preparing for Standardized Tests............................................................628

• Meteorologist..............................................623

• Multiple Choice ..........591, 597, 605, 611, 622• Open Ended................................................617

• Paper Folding................................................593

• Research..........................................................585• Data Update....................................................622• Career Data.................................................623• Review Activities .......................................624• Test Practice ................................................629

..................608

..........................586, 587, 592, 594, 600, 602,605, 606, 608, 612, 617


TP

NQ

R

Chapter 15 Formalizing Proof............................................................................................630

Check Your Readiness..........................................................................63115–1 Logic and Truth Tables...............................................................................63215– 2 Deductive Reasoning............................................................................63815– 3 Paragraph Proofs...................................................................................644

Quiz 1: Lessons 15–1 through 15–3...................................................64815– 4 Preparing for Two-Column Proofs.....................................................64915– 5 Two-Column Proofs..............................................................................654

Quiz 2: Lessons 15–4 and 15–5................................................................65915– 6 Coordinate Proofs ......................................................................................660

Investigation: Don’t Touch the Poison Ivy..........................................666


• Open Ended.......................................................................637, 659• Multiple Choice.......................................................643, 648, 653, 665

......................................................660

• Research..........................................................631• Data Update..............................................653• Review Activities...........................................668• Test Practice ...................................................673


Investigation, page 666

More Coordinate Graphing and Transformations........................................................................674

Check Your Readiness..........................................................................67516–1 Solving Systems of Equations by Graphing........................................67616–2 Solving Systems of Equations by Using Algebra.............................681

Quiz 1: Lessons 16–1 and 16–2............................................................... 68616–3 Translations ............................................................................................68716–4 Reflections....................................................................................................69216–5 Rotations.................................................................................................697

Quiz 2: Lessons 16–3 through 16–5.....................................................70216–6 Dilations..................................................................................................703

Investigation: Artists Do Math, Don’t They? ...................................708

ASSESSMENTStudy Guide and Assessment ...............................................................710Chapter Test...................................................................................................713Preparing for Standardized Tests .................................................................714

• Animator...................................................691

• Multiple Choice..........680, 690, 696, 702, 707• Open Ended................................................686

................692

• Research..........................................................675• Data Update..............................................680• Career Data.................................................691• Review Activities .......................................710• Test Practice ................................................715

.................700

...........................................................694, 696


xxiii

Chapter 16


1 Number Concept Problems 46– 472 More Number Concept Problems 86–873 Counting and Probability Problems 138 –1394 Data Analysis Problems 184–1855 Statistics Problems 224– 2256 Algebra Problems 272 – 2737 Algebra Word Problems 306– 3078 Coordinate Geometry Problems 346– 3479 Ratio and Proportion Problems 398 – 399

10 Triangle and Quadrilateral Problems 450 – 45111 Function Problems 492 – 49312 Angle, Line, and Arc Problems 544– 54513 Perimeter, Circumference, and Area Problems 582 – 58314 Right Triangle and Trigonometry Problems 628 – 62915 Solid Figure Problems 672 – 67316 Systems of Equations and Polynomial Problems 714– 715

Preparing for Standardized Test Success

xxiv

With some practice, studying, and review, you will be ready forstandardized test success. Good luck from Glencoe/McGraw-Hill!

The Preparing for Standardized Tests pages are part of a complete testpreparation course offered in this text. The test items on these pages werewritten in the same style as those in state proficiency tests and standardizedtests like ACT and SAT. The 16 topics are closely aligned with those tests, thegeometry curriculum, and this text. These topics cover all of the types ofproblems you will see on these tests.

Chapter Mathematics Topic Pages

The Preparing for Standardized Tests pagesat the end of each chapter and at the end of thebook have been created to help you get readyfor the mathematics portions of yourstandardized tests. On these pages, you willfind strategies for solving problems and test-taking advice to help you maximize your score.

It is important to remember that there aremany different standardized tests given byschools and states across the country. Find outas much as you can about your test. Start byasking your teacher and counselor for anyinformation, including practice materials, thatmay be available to help you prepare.

To help you get ready for these tests, do the Standardized Test Practice question in eachlesson. Also review the concepts andtechniques contained in the Preparing forStandardized Tests pages at the end of eachchapter listed below. This will help you becomefamiliar with the types of math questions thatare asked on various standardized tests.

The Preparing for Standardized Tests pages inthe Student Handbook review common typesof problems on standardized tests and providepractice for each format.

1

Tool Keystrokes

Alpha-Num 2

Angle 4 3

Angle Bisector 4

Area 4 2

Calculate 6

Circle 4

Clear 7

Comment 5

Compass 6

Coordinates & Equation 5

Dilation 5

Distance & Length 3 1

Hide/Show 1

Intersection Point 3

Line 2F2

F2

F5

F5

F4

F5

F3

F4

F5

F2

F5

F5

F3

F5

F5

Tool Keystrokes

Locus 7

Midpoint 5

Parallel Line 2

Perpendicular Bisector 3

Perpendicular Line 1

Point 1

Point on Object 2

Reflection 2

Rotation 4

Segment 3

Slope 4 4

Symmetry 1

Translation 3

Triangle 5F2

F4

F4

F5

F2

F4

F4

F2

F2

F3

F3

F3

F3

F3

Throughout this text, Graphing Calculator Explorations have been includ-ed so you can use technology to solve problems. These activities use theTI–83 Plus or TI–84 Plus graphing calculator.

The TI–83 Plus/TI–84 Plus has a wide variety of applications and features.If you are just beginning to use the calculator, you will not need to use all of its features. This page is designed to be a quick reference for the features you will need to use as you study from this text.

To open a geometry session: (Name)

To quit a menu: ESC

ENTERAPPS

Graphing Calculator Quick Reference Guide

Documents

Table of Contents - Glencoeglencoe.com/sec/math/ose/geoca/2006/docs/contents.pdf · Table Of Contents. Segment Measure and Coordinate Graphing.....48 Check Your Readiness