AMSCO'S Geometry. New York - Rye High School

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326 Slopes and Equations of LinesPart IIAnswer all questions in this part. Each correct answer will receive 2 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.11. a. Draw ABC in the coordinate plane if the coordinates of A are (3, 1),of B are (1, 5), and of C are (5, 2).b. Under a translation, the image of A is A(1, 1). Draw ABC, theimage of ABC under this translation, and give the coordinates of Band C.c. If this translation can be written as (x, y) → (x a, y b), what are thevalues of a and b?12. The coordinates of the vertices of DEF are D(1, 6), E(3, 3), andF(1, 2). Is DEF a right triangle? Justify your answer.Part IIIAnswer all questions in this part. Each correct answer will receive 4 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.13. In the diagram, TQ hbisects RTS andTQ ' RS. Prove that RST is isosceles.14. The following statements are true:• If Evanston is not the capital ofIllinois, then Chicago is not the capital.• Springfield is the capital of Illinois orChicago is the capital of Illinois.• Evanston is not the capital of Illinois.Use the laws of logic to prove thatSpringfield is the capital of Illinois.TRQS
Cumulative Review 327Part IVAnswer all questions in this part. Each correct answer will receive 6 credits.Clearly indicate the necessary steps, including appropriate formula substitutions,diagrams, graphs, charts, etc. For all questions in this part, a correct numericalanswer with no work shown will receive only 1 credit.15. Find the coordinates of the point of intersection of the lines whose equationsare y 3x 1 and x 2y 5.16. Given: CGF and DGE bisect each other at G.Prove: CD > FE
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AMSCO’SGEOMETRYAnn Xavier Gantert
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PREFACE✔✔✔✔✔✔Geometry i
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CONTENTSChapter 1ESSENTIALS OF GEOM
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viiiCONTENTSReview Exercises 323Cum
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xCONTENTS14-3 Five Fundamental Loci
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2 Essentials of Geometry1-1 UNDEFIN
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4 Essentials of GeometryThe number
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6 Essentials of GeometryEXAMPLE 1In
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8 Essentials of GeometryRecall that
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10 Essentials of GeometryEXAMPLE 1O
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12 Essentials of GeometryOn the num
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14 Essentials of Geometry7. A, B, C
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16 Essentials of Geometry1. By a ca
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18 Essentials of GeometrySolutiona.
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20 Essentials of GeometryBisector o
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22 Essentials of GeometryIn 11-13,
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24 Essentials of GeometryIncluded S
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26 Essentials of GeometryRight Tria
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28 Essentials of GeometryIn 5 and 6
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30 Essentials of GeometryPR S TProp
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32 Essentials of Geometry12. In iso
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CHAPTER2CHAPTERTABLE OF CONTENTS2-1
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36 LogicSome sentences are true for
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38 LogicNegationsIn the study of lo
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40 Logic2. a. Give an example of a
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42 Logic2-2 CONJUNCTIONSWe have ide
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44 LogicA compound sentence may con
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46 LogicEXAMPLE 4Three sentences ar
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48 Logic31. I have the hiccups and
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50 LogicAnswers(1) k ∨ q a. Every
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52 Logic8. A gram is a measure of l
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54 LogicParts of a ConditionalThe p
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56 Logic2. “In order to succeed,
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58 LogicExercisesWriting About Math
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60 Logic42. The conditional p → q
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62 Logicp: Angle A and B are congru
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64 LogicOn Friday, p is true and q
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66 LogicConditional If Jessica like
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68 LogicIn 7-10: a. Write the inver
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70 LogicRecall that a conjunction i
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72 LogicEXAMPLE 2The statement “I
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74 LogicApplying Skills17. Let p re
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76 LogicThe Law of Disjunctive Infe
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78 Logic(1) Eliminate the second ro
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80 Logic17. If 2b 6 14, then 2b
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82 Logicglass” is also true. Appl
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84 Logic7. When p → q and p ∧ q
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86 Logic•A hypothesis, also calle
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88 Logic8. July is a winter month i
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90 LogicExploration1. A tautology i
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92 Logic11. The first two sentences
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94 Proving Statements in Geometry3-
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96 Proving Statements in GeometryDe
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98 Proving Statements in GeometryBe
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100 Proving Statements in Geometry1
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102 Proving Statements in GeometryE
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104 Proving Statements in GeometryA
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108 Proving Statements in GeometryC
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110 Proving Statements in GeometryS
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116 Proving Statements in GeometryF
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120 Proving Statements in GeometryJ
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128 Proving Statements in GeometryC
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CHAPTER1344CHAPTERTABLE OF CONTENTS
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136 Congruence of Line Segments,Ang
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CHAPTER1745CHAPTERTABLE OF CONTENTS
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176 Congruence Based on TrianglesAC
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178 Congruence Based on Triangles6.
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180 Congruence Based on TrianglesDe
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182 Congruence Based on TrianglesTh
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184 Congruence Based on Triangles(C
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186 Congruence Based on Triangles5-
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196 Congruence Based on TrianglesAp
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198 Congruence Based on TrianglesCo
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200 Congruence Based on TrianglesCo
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202 Congruence Based on TrianglesEX
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204 Congruence Based on TrianglesCH
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206 Congruence Based on TrianglesCU
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208 Congruence Based on Triangles13
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210 Transformations and the Coordin
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CHAPTER7CHAPTERTABLE OF CONTENTS7-1
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264 Geometric InequalitiesThis corr
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266 Geometric InequalitiesExercises
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268 Geometric InequalitiesSubtracti
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270 Geometric Inequalities7-3 INEQU
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272 Geometric InequalitiesExercises
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274 Geometric InequalitiesEXAMPLE 2
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Page 288 and 289: 278 Geometric InequalitiesABMCProof
Page 290 and 291: 280 Geometric InequalitiesExercises
Page 292 and 293: 282 Geometric InequalitiesGivenTo p
Page 294 and 295: 284 Geometric InequalitiesCIf the m
Page 296 and 297: 286 Geometric Inequalities7.3 If th
Page 298 and 299: 288 Geometric InequalitiesCUMULATIV
Page 300 and 301: CHAPTER2908CHAPTERTABLE OF CONTENTS
Page 302: 292 Slopes and Equations of LinesAl
Page 305 and 306: Developing SkillsIn 3-11, in each c
Page 307 and 308: y 2 bx 2 a 5 m The Equation of a Li
Page 309 and 310: 5 ? 3 2(2) 1 1 5 ? 2(0) 1 7 5 ? 2
Page 311 and 312: zontal line, they all have the same
Page 313 and 314: Midpoint of a Line Segment 303Proof
Page 315 and 316: Midpoint of a Line Segment 305EXAMP
Page 317 and 318: The Slopes of Perpendicular Lines 3
Page 319 and 320: The Slopes of Perpendicular Lines 3
Page 321 and 322: Developing SkillsIn 3-12: a. Find t
Page 323 and 324: Coordinate Proof 3138-5 COORDINATE
Page 325 and 326: Coordinate Proof 315ProofThis is a
Page 327 and 328: Concurrence of the Altitudes of a T
Page 333 and 334: VOCABULARY8-1 Slope • x • y8-2
Page 335: Cumulative Review 325CUMULATIVE REV
Page 339 and 340: Proving Lines Parallel 3299-1 PROVI
Page 341 and 342: Proving Lines Parallel 331In the di
Page 343 and 344: Proving Lines Parallel 333The proof
Page 345 and 346: Properties of Parallel Lines 3359-2
Page 347 and 348: Properties of Parallel Lines 337The
Page 349 and 350: gEJ. Therefore, AB g CD gbecause i
Page 351 and 352: c. Is the measure of an exterior an
Page 353 and 354: Parallel Lines in the Coordinate Pl
Page 355 and 356: Parallel Lines in the Coordinate Pl
Page 357 and 358: . Find the midpoints of two sides o
Page 359 and 360: The Sum of the Measures of the Angl
Page 361 and 362: The Sum of the Measures of the Angl
Page 363 and 364: Proving Triangles Congruent by Angl
Page 365 and 366: Proving Triangles Congruent by Angl
Page 367 and 368: The Converse of the Isosceles Trian
Page 369 and 370: The Converse of the Isosceles Trian
Page 371 and 372: In 3-6, in each case the degree mea
Page 373 and 374: (1) Since any line segment may beex
Page 375 and 376: Proving Right Triangles Congruent b
Page 377 and 378: Interior and Exterior Angles of Pol
Page 383 and 384: Chapter Summary 373CHAPTER SUMMARYD
Page 385 and 386: AB g In 1-5, CD gand these lines a
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2. The statement “If two angles f
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CHAPTERQUADRILATERALSEuclid’s fif
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The Parallelogram 381ADBCQuadrilate
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The Parallelogram 383DEFINITIONThe
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Proving That a Quadrilateral Is a P
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Proving That a Quadrilateral Is a P
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The Rectangle 38910-4 THE RECTANGLE
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The Rectangle 391EXAMPLE 1Given: AB
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The Rhombus 39316. The coordinates
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The Rhombus 395Theorem 10.15If a qu
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2. Concepta said that if the length
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The Square 39910-6 THE SQUAREDEFINI
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The Square 401EXAMPLE 2In square PQ
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The Trapezoid 403The Isosceles Trap
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The Trapezoid 405Proof We will show
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The Trapezoid 407The slopes of BC a
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18. Prove Theorem 10.23, “The len
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Areas of Polygons 4115. Find the ar
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Chapter Summary 413PostulateTheorem
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Review Exercises 41511. The diagona
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Cumulative Review 417CUMULATIVE REV
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CHAPTERTHEGEOMETRYOF THREEDIMENSION
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Points, Lines, and Planes 421Theore
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Perpendicular Lines and Planes 4231
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Perpendicular Lines and Planes 425G
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Perpendicular Lines and Planes 427l
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Perpendicular Lines and Planes 429G
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gPlanes p and q intersect in AB. In
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16. Prove that if two points are ea
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Parallel Lines and Planes 435Theore
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BF intersecting q at . Since p and
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ProofTwo lines perpendicular to the
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Since the bases are parallel, the c
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Surface Area of a Prism 443EXAMPLE
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10. A prism has bases that are trap
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Volume of a Prism 447The other pris
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Pyramids 44911-6 PYRAMIDSA pyramid
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Pyramids 451For example, consider a
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Cylinders 45314. Let F be the verte
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Express this result as a rational a
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Cones 457We can make a model of a r
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7. The volume of a cone is 127 cubi
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Spheres 461Proof Statements Reasons
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Spheres 463When we round to the nea
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Chapter Summary 465• Perpendicula
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Vocabulary 46711.14 The intersectio
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Review Exercises 46914. A prism and
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Cumulative Review 471b. Using the s
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Cumulative Review 47314. Line segme
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Ratio and Proportion 47512-1 RATIO
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Ratio and Proportion 477ProofWe can
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Ratio and Proportion 479EXAMPLE 3Th
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Given ABC, D is the midpoint of AC,
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Proportions Involving Line Segments
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Proportions Involving Line Segments
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If two polygons are similar, then t
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Proving Triangles Similar 4899. Tri
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Proving Triangles Similar 491We can
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Proving Triangles Similar 493EXAMPL
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Dilations 49511. If CA 48, DA 12,
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Dilations 497Slope ofAB 5 d b 2 2 a
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EXAMPLE 2SolutionDilations 499Find
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Dilations 50129. The vertices of oc
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Proportional Relations Among Segmen
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Proportional Relations Among Segmen
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Concurrence of the Medians of a Tri
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(2) Find the equation of AM g and t
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Proportions in a Right Triangle 511
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Proportions in a Right Triangle 513
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Pythagorean Theorem 51512-9 PYTHAGO
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Pythagorean Theorem 517EXAMPLE 2Whe
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Pythagorean Theorem 519EXAMPLE 3In
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The Distance Formula 52123. A young
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The lengths of the sides of the qua
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Developing SkillsIn 3-10, the coord
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Chapter Summary 527CHAPTER SUMMARYD
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Review Exercises 529FormulasIn the
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14. The length of a side of a rhomb
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Cumulative Review 5334. The measure
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CHAPTERGEOMETRYOF THECIRCLEEarly ge
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Arcs and Angles 537In the diagram,
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If (O > (Or and mCDX 5 mCrDr 60, t
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Arcs and Angles 541b. mACX mAOC 75
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Arcs and Chords 54313-2 ARCS AND CH
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Arcs and Chords 545ProofFirst draw
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Arcs and Chords 547Since a diameter
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Arcs and Chords 549(5) Since AB CD
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Arcs and Chords 551EXAMPLE 3ProofPr
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Inscribed Angles and Their Measures
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. m/A 5 X 12 mBC c. m/C 5 180 2 (m/
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Inscribed Angles and Their Measures
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Tangents and Secants 559Theorem 13.
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ProofTangents and Secants 561We wil
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Tangents and Secants 563The proofs
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Developing SkillsIn 3 and 4, ABC is
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Hands-On ActivityConsider any regul
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Angles Formed by Tangents, Chords,
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Measures of Tangent Segments, Chord
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Circles in the Coordinate Plane 581
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T 3, 22lation :Circles in the Coord
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Developing SkillsIn 3-8, write an e
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Circles in the Coordinate Plane 587
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How to Proceed(1) Solve the pair of
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Tangents and Secants in the Coordin
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Chapter Summary 59321. a. Write an
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Chapter Summary 59513.12 The measur
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Vocabulary 597Formulas(Continued)Ty
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Review Exercises 59911. Two circles
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Cumulative Review 6012. The coordin
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Find the coordinatesR 90+ r y5x.Cum
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Constructing Parallel Lines 60514-1
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Constructing Parallel Lines 607Exer
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PL h b. Choose point N on . Constru
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The Meaning of Locus 611Note that i
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Five Fundamental Loci 613Applying S
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SolutionAnswerBCAB g CD g . The lo
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Points at a Fixed Distance in Coord
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Equidistant Lines in Coordinate Geo
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Points Equidistant from a Point and
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Review Exercises 631VOCABULARY14-2
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CUMULATIVE REVIEW Chapters 1-14Part
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Part IVAnswer all questions in this
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Index 637Biconditional(s), 69-73app
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Index 639multiplicative, 5Identity
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Index 641Projectionof point on a li
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Index 643Trichotomy postulate, 264-
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AMSCO'S Geometry. New York - Rye High School

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