AMSCO'S Geometry. New York - Rye High School

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CONTENTSviiReview Exercises 204Cumulative Review 206Chapter 6TRANSFORMATIONS AND THE COORDINATE PLANE 2096-1 The Coordinates of a Point in a Plane 2106-2 Line Reflections 2146-3 Line Reflections in the Coordinate Plane 2226-4 Point Reflections in the Coordinate Plane 2276-5 Translations in the Coordinate Plane 2326-6 Rotations in the Coordinate Plane 2386-7 Glide Reflections 2436-8 Dilations in the Coordinate Plane 2476-9 Transformations as Functions 250Chapter Summary 255Vocabulary 257Review Exercises 257Cumulative Review 259Chapter 7GEOMETRIC INEQUALITIES 2627-1 Basic Inequality Postulates 2637-2 Inequality Postulates Involving Addition and Subtraction 2677-3 Inequality Postulates Involving Multiplication and Division 2707-4 An Inequality Involving the Lengths of the Sides of a Triangle 2737-5 An Inequality Involving an Exterior Angle of a Triangle 2767-6 Inequalities Involving Sides and Angles of a Triangle 281Chapter Summary 285Vocabulary 286Review Exercises 286Cumulative Review 288Chapter 8SLOPES AND EQUATIONS OF LINES 2908-1 The Slope of a Line 2918-2 The Equation of a Line 2958-3 Midpoint of a Line Segment 3008-4 The Slopes of Perpendicular Lines 3078-5 Coordinate Proof 3138-6 Concurrence of the Altitudes of a Triangle 317Chapter Summary 322Vocabulary 323
Page 1 and 2: AMSCO’SGEOMETRYAnn Xavier Gantert
Page 3 and 4: PREFACE✔✔✔✔✔✔Geometry i
Page 5: CONTENTSChapter 1ESSENTIALS OF GEOM
Page 9 and 10: CONTENTSix11-8 Spheres 459Chapter S
Page 11 and 12: CHAPTERESSENTIALSOF GEOMETRYFor tho
Page 13 and 14: The Real Numbers and Their Properti
Page 15 and 16: The Real Numbers and Their Properti
Page 17 and 18: Definitions, Lines, and Line Segmen
Page 19 and 20: Definitions, Lines, and Line Segmen
Page 21 and 22: In 8-13, use the number line to fin
Page 23 and 24: Midpoints and Bisectors 13We can al
Page 25 and 26: ABB A OEvery point on a line divide
Page 27 and 28: Classifying Angles According to The
Page 29 and 30: More Angle Definitions 195. For the
Page 31 and 32: EXAMPLE 1SolutionSP hIn the figure,
Page 33 and 34: 28. bisects QRS. If mQRS 10x and m
Page 35 and 36: Triangles 25DEFINITIONA scalene tri
Page 37 and 38: EXAMPLE 2(1) PR g is a straight lin
Page 39 and 40: Chapter Summary 29CHAPTER SUMMARYUn
Page 41 and 42: Review Exercises 31property of addi
Page 43 and 44: Review Exercises 331. Draw a point
Page 45 and 46: Sentences, Statements, and Truth Va
Page 53 and 54: Conjunctions 43STEP 1. In the first
Page 55 and 56: Conjunctions 45(3) The statement is
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9. The sky is not cloudy and it is
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Disjunctions 494. On Thursday, it r
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Disjunctions 51Two Uses of the Word
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31. Nicolette is my friend or Miche
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Conditionals 55CASE 2You get an A i
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Conditionals 57(3) If 12 is a multi
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In 17-24, for each given statement:
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Inverses, Converses, and Contraposi
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2. A false conditional can have a f
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26. Which is the converse of “If
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Biconditionals 71For example:p: 3x
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Biconditionals 73SolutionWhen y = 9
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The Laws of Logic 75The Law of Deta
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The Laws of Logic 77Make a truth ta
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The Laws of Logic 79ExercisesWritin
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Drawing Conclusions 81Since “Rach
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Drawing Conclusions 83(1) Since Ted
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Chapter Summary 8515. Taylor, Melis
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Review Exercises 87Laws of Logic•
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Review Exercises 89• Janice is 26
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Cumulative Review 913. Points J, K,
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CHAPTERPROVINGSTATEMENTS INGEOMETRY
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periments, you can arrive at a gene
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Applying SkillsIn 13-16, state in e
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Definitions as Biconditionals 99Sol
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Deductive Reasoning 101ABCIn the lo
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Deductive Reasoning 103• The bise
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Direct and Indirect Proofs 10517. I
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Direct and Indirect Proofs 107State
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Postulates,Theorems, and Proof 1093
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Postulates,Theorems, and Proof 111F
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Postulates,Theorems, and Proof 113E
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The Substitution Postulate 11511. E
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The Substitution Postulate 117EXAMP
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The Addition and Subtraction Postul
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The Multiplication and Division Pos
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Developing SkillsIn 3 and 4, in eac
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Review Exercises 1293-3 Proof • D
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Cumulative Review 131CUMULATIVE REV
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BD h 15. bisects ABC,mABD 3x 18 a
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Postulates of Lines, Line Segments,
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Postulates of Lines, Line Segments,
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Prove: BD h ' AC gIn geometry, we a
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Using Postulates and Definitions in
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Using Postulates and Definitions in
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Proving Theorems About Angles 145Th
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Proving Theorems About Angles 147Pr
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ProofIn the figure, ABC and CBD for
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Proving Theorems About Angles 1514.
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Proving Theorems About Angles 153h
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Congruent Polygons and Correspondin
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Congruent Polygons and Correspondin
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Proving Triangles Congruent Using S
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Proving Triangles Congruent Using A
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Proving Triangles Congruent Using A
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Proving Triangles Congruent Using S
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Chapter Summary 16712. C13. D C 14.
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Review Exercises 169VOCABULARY4-1 D
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2. If the sum of the measures of tw
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Cumulative Review 173Part IVAnswer
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Line Segments Associated with Trian
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Line Segments Associated with Trian
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EXAMPLE 1Using Congruent Triangles
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Isosceles and Equilateral Triangles
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Using Two Pairs of Congruent Triang
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Proving Overlapping Triangles Congr
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Perpendicular Bisector of a Line Se
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Basic Constructions 197ConclusionCD
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Basic Constructions 199Construction
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Basic Constructions 201Construction
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Basic Constructions 2035. Given: Li
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Review Exercises 2053. In ABC, CD i
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8. Which of the following is not an
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CHAPTERTRANSFORMATIONSAND THECOORDI
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The Coordinates of a Point in a Pla
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The Coordinates of a Point in a Pla
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Line Reflections 215SSDEFINITIONA t
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Line Reflections 217Corollary 6.1aU
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Line Reflections 2193. The angles o
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Line Reflections 221Developing Skil
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Line Reflections in the Coordinate
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Line Reflections in the Coordinate
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For each figure, construct the refl
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BPAPoint Reflections in the Coordin
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Point Reflections in the Coordinate
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Translations in the Coordinate Plan
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Rotations in the Coordinate Plane 2
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ccRotations in the Coordinate Plane
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Developing SkillsFor 3 and 4, refer
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Glide Reflections 245Solution a. r
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Dilations in the Coordinate Plane 2
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Dilations in the Coordinate Plane 2
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Transformations as Functions 251f:
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EXAMPLE 1r x-axis+ r y-axisand sket
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Chapter Summary 25514. The vertices
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Review Exercises 2576.2 Under a ref
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ExplorationCumulative Review 259Des
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Cumulative Review 261Part IVAnswer
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Basic Inequality Postulates 2637-1
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Basic Inequality Postulates 265EXAM
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Inequality Postulates Involving Add
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Inequality Postulates Involving Add
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Inequality Postulates Involving Mul
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An Inequality Involving the Lengths
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An Inequality Involving the Lengths
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An Inequality Involving an Exterior
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An Inequality Involving an Exterior
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Inequalities Involving Sides and An
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Inequalities Involving Sides and An
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Chapter Summary 285Applying SkillsC
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Review Exercises 28711. In isoscele
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Cumulative Review 289Part IIAnswer
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The Slope of a Line 2918-1 THE SLOP
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294 Slopes and Equations of LinesEX
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296 Slopes and Equations of LinesTh
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298 Slopes and Equations of LinesSo
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300 Slopes and Equations of Lines16
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302 Slopes and Equations of LinesNo
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304 Slopes and Equations of LinesAD
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306 Slopes and Equations of LinesEx
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308 Slopes and Equations of LinesPr
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310 Slopes and Equations of LinesWe
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312 Slopes and Equations of Lines27
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314 Slopes and Equations of LinesEX
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316 Slopes and Equations of Lines4.
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318 Slopes and Equations of LinesyB
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320 Slopes and Equations of LinesTh
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322 Slopes and Equations of Linesd.
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324 Slopes and Equations of Lines8.
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326 Slopes and Equations of LinesPa
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CHAPTER9CHAPTERTABLE OF CONTENTS9-1
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330 Parallel LinesEXAMPLE 1If line
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332 Parallel LinesGiven EF ginterse
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334 Parallel LinesExercisesWriting
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336 Parallel LinesProofWe can use a
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338 Parallel Linesc. Since GHC and
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340 Parallel LinesNote: In the diag
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342 Parallel Lines9-3 PARALLEL LINE
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344 Parallel LinesSolution22 2 (24)
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346 Parallel Lines14. In quadrilate
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348 Parallel LinesCorollary 9.11aIf
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350 Parallel LinesSubstitute x 8 i
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352 Parallel Lines25. The measure o
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354 Parallel LinesEXAMPLE 1Prove th
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356 Parallel LinesExercisesWriting
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358 Parallel LinesGivenProveABC wit
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360 Parallel LinesEXAMPLE 3Given: Q
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362 Parallel Lines18. Given: BE hbi
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364 Parallel LinesConcurrence of An
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366 Parallel Lines4. Triangle ABC i
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368 Parallel LinesA convex polygon
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370 Parallel LinesEXAMPLE 1The meas
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372 Parallel Lines15. Find the numb
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374 Parallel Lines9.11f The measure
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376 Parallel Lines18. If parallel l
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378 Parallel LinesPart IIAnswer all
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380 Quadrilaterals10-1 THE GENERAL
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382 QuadrilateralsWe can think of e
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384 QuadrilateralsDeveloping Skills
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386 QuadrilateralsTheorem 10.6If bo
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388 Quadrilaterals8. ABCD is a quad
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390 QuadrilateralsProperties of a R
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392 QuadrilateralsExercisesWriting
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394 QuadrilateralsTheorem 10.13The
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396 QuadrilateralsSPProof Since all
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398 Quadrilaterals18. The vertices
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400 QuadrilateralsTheorem 10.19If o
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402 Quadrilaterals10. If a quadrila
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404 Quadrilaterals(Continued)Statem
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406 QuadrilateralsProofy D(d, e) C(
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408 QuadrilateralsExercisesWriting
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410 QuadrilateralsEXAMPLE 1' ABCD i
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412 Quadrilaterals15. The altitude
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414 Quadrilaterals10-4 Rectangle10-
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416 QuadrilateralsExplorationIn Cha
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418 QuadrilateralsPart IIAnswer all
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420 The Geometry of Three Dimension
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CHAPTER47412CHAPTERTABLE OF CONTENT
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476 Ratio, Proportion, and Similari
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536 Geometry of the Circle13-1 ARCS
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538 Geometry of the CircleF8080GOEI
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540 Geometry of the CircleTheorem 1
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542 Geometry of the CircleIn 23-32,
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544 Geometry of the CircleProofWe w
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546 Geometry of the CircleChords Eq
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548 Geometry of the CircleThe conve
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550 Geometry of the CircleA90°6 CO
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552 Geometry of the Circle18. If AB
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554 Geometry of the CircleCorollary
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556 Geometry of the Circle2. In cir
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558 Geometry of the Circle30. Point
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560 Geometry of the CircleIn the di
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562 Geometry of the CircleGiven PQ
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564 Geometry of the CircleEXAMPLE 4
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566 Geometry of the CircleApplying
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568 Geometry of the CircleWe can st
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572 Geometry of the CircleSUMMARY (
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574 Geometry of the Circle28. Tange
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576 Geometry of the CircleCAOBWe wi
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578 Geometry of the CirclePSolution
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580 Geometry of the CircleDevelopin
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582 Geometry of the CircleLet the i
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586 Geometry of the Circle27. 2x 2
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588 Geometry of the Circle13-8 TANG
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592 Geometry of the CircleExercises
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594 Geometry of the CirclePostulate
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596 Geometry of the CircleFormulas(
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598 Geometry of the Circle13-4 Tang
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600 Geometry of the CircleIn this e
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602 Geometry of the CirclePart IIAn
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CHAPTER14CHAPTERTABLE OF CONTENTS14
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606 Locus and ConstructionConstruct
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608 Locus and Construction6. Given:
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610 Locus and ConstructionDiscoveri
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612 Locus and ConstructionExercises
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614 Locus and Construction3. Equidi
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616 Locus and Construction4. The lo
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618 Locus and ConstructionMETHOD 1
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620 Locus and Constructionmidpoint
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622 Locus and ConstructionyOB(a, a)
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624 Locus and Construction20. Show
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626 Locus and ConstructionEXAMPLE 1
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628 Locus and ConstructionEXAMPLE 3
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630 Locus and ConstructionHands-On
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632 Locus and ConstructionIn 15-18,
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634 Locus and Construction9. The al
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INDEXAAA triangle similarity (AA),
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638 IndexDefinition(s) cont.using,
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640 IndexMedian cont.of triangle, 1
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642 IndexSimilarityequivalence rela
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AMSCO'S Geometry. New York - Rye High School

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