Reasoning in Geometry....................................................................................2 Check Your Readiness .......................................................................................... 3 1–1 Patterns and Inductive Reasoning .............................................................4 Investigation: To Grandmother’s House We Go! ...............................10 1–2 Points, Lines, and Planes............................................................................12 Quiz 1: Lessons 1–1 and 1–2 .......................................................................17 1–3 Postulates..................................................................................................18 1– 4 Conditional Statements and Their Converses ........................................ 24 Quiz 2: Lessons 1– 3 and 1– 4......................................................................28 1–5 Tools of the Trade .........................................................................................29 1–6 A Plan for Problem Solving .......................................................................35 ASSESSMENT Study Guide and Assessment ....................................................................42 Chapter Test .....................................................................................................45 Preparing 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
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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
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
ASSESSMENTStudy Guide and Assessment ....................................................................82Chapter Test .....................................................................................................85Preparing for Standardized Tests ..............................................................86
• Multiple Choice ..................................................................55, 61, 67, 73• Open Ended.........................................................................................81
• Research................................................................................................49• Data Update.........................................................................................55• Review Activities...........................................................................82• Test Practice ....................................................................................87
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
ASSESSMENTStudy Guide and Assessment ..................................................................134Chapter Test...................................................................................................137Preparing for Standardized Tests .................................................................138
• Research.........................................................89• Career Data..............................................95, 115• Data Update................................................101• Review Activities..........................................134• Test Practice ..............................................139
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 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
Triangles and Congruence ..................................................................186
Check Your Readiness..........................................................................1875–1 Classifying Triangles...................................................................................1885–2 Angles of a Triangle..............................................................................1935–3 Geometry in Motion..................................................................................198
Investigation: Take a Shortcut...............................................................2085–5 SSS and SAS .......................................................................................210
Quiz 2: Lessons 5 – 4 and 5 –5 ....................................................................2145–6 ASA and AAS..............................................................................................215
ASSESSMENTStudy Guide and Assessment ..................................................................220Chapter Test...................................................................................................223Preparing for Standardized Tests .................................................................224
• Multiple Choice..........192, 202, 207, 214, 219• Open Ended................................................197
..................203• Construction .............................................210
• Research.......................................................187• Data Update................................................191• Review Activities..........................................220• Test Practice ...................................................225
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
• Research...............................................................227• Data Update ..................................................255• Review Activities ..........................................268• Test Practice ........................................................273
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
ASSESSMENTStudy Guide and Assessment ..................................................................302Chapter Test...................................................................................................305Preparing for Standardized Tests ............................................................306
• Multiple Choice..........................281, 287, 300• Open Ended................................................295
.................283
• Research.......................................................275• Data Update................................................277• Career Data ....................................................301• Review Activities..........................................302• Test Practice ...................................................307
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
• 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
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
ASSESSMENTStudy Guide and Assessment ..................................................................394Chapter Test...................................................................................................397Preparing for Standardized Tests ............................................................398
• Research..........................................................349• Data Update....................................................354• Career Data.................................................379• Review Activities .......................................394• Test Practice ................................................399
...................371
..........355, 362, 368, 380, 381, 382, 393
Standardized Test Practice
xvi
Chapter 9
Lesson 9–5, page 379
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
ASSESSMENTStudy Guide and Assessment ..................................................................446Chapter Test...................................................................................................449Preparing for Standardized Tests .................................................................450
• Research..............................................................................................401• Data Update ..............................................................................414• Career Data........................................................................431, 445• Review Activities.........................................................................446• Test Practice ..................................................................................451
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
ASSESSMENTStudy Guide and Assessment ..................................................................488Chapter Test...................................................................................................491Preparing for Standardized Tests ............................................................492
• 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
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
ASSESSMENTStudy Guide and Assessment ..................................................................540Chapter Test...................................................................................................543Preparing for Standardized Tests ............................................................544
• Multiple Choice......................................501, 509, 515, 521, 533, 539• Open Ended.......................................................................................527
• Research..........................................................495• Data Update..............................................530• Review Activities ...........................................540• Test Practice ...................................................545
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
ASSESSMENTStudy Guide and Assessment ..................................................................578Chapter Test...................................................................................................581Preparing for Standardized Tests ............................................................582
• Multiple Choice.......................................................553, 563, 569, 577• Open Ended.......................................................................................558
• Research..............................................................................................547• Data Update .................................................................................561• Review Activities.........................................................................578• Test Practice ..................................................................................583
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 2: Lessons 14–4 and 14–5............................................................... 61714– 6 Equations of Circles...................................................................................618
ASSESSMENTStudy Guide and Assessment ..................................................................624Chapter Test...................................................................................................627Preparing for Standardized Tests............................................................628
• 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
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
ASSESSMENTStudy Guide and Assessment ..................................................................668Chapter Test...................................................................................................671Preparing for Standardized Tests ............................................................672
• Open Ended.......................................................................637, 659• Multiple Choice.......................................................643, 648, 653, 665
• Research..........................................................631• Data Update..............................................653• Review Activities...........................................668• Test Practice ...................................................673
Standardized Test Practice
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 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
• 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
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.