WPC! ?D~Qsqz[h kC&I"4 4V cy:Osc4]"P&.w.Bwچnt w^ _L'V oUѸ :Nbdoc爼q]iP8W" J k[?y]w640h>D'Igڃ{"pFI@Kp|RPaƋr?ck`<v7G8u[H$[I$P.2)Pq:by+J{pr>9Ρiל!{-.AۯͲnCbh05 s;#Q8^2) uhB .-!±2|M/7~m5N#ݮ55TpzIH=@MLo~FeYJ( r ^]#UN %% 0(+ 4S g Nv wx | m~ ^ U@ @ o p: AY(  0DG! 0F!\\WNTPRINT\LDB4390(9 Z 6Times New Roman RegularX($E]+@8P!%<3|xU+s (9 Z(Times New Roman *OLE*WPC..!. S  .1   & & MathType "-<@<<<C Times New Roman?- 2 lx 2 y [Times New Roman- 2 =2p 2 2pTimes New Roman- 2 4 2 9 2 1Symbol- 2 S+ 2 = & "System-WPWin 6.0/OLE 1.0 Prefix Information MarkerEquation.COEE2ࡱ> Root EntryF`}{Ole CompObjjBOlePart  FMicrosoft Equation 2.0 DS EquationEquation.COEE29q S  .1   & & MathType "-<@<<<OlePres000Equation Native hC Times New Roman?- 2 lx 2 y [Times New Roman- 2 =2p 2 2pTimes New Roman- 2 4 2 9 2 1Symbol- 2 S+ 2 = & "System-L6JD x 2 4+y 2 9=1 METAFILEPICTt S  .1   & & MathType "-<@<<<C Times New Roman?- 2 lx 2 y [Times New Roman- 2 =2p 2 2pTimes New Roman- 2 4 2 9 2 1Symbol- 2 S+ 2 = & "System-Z[\O  , deUULevel 1Level 2Level 3Level 4Level 5(3$ !  (n$ (  1  ) !  _Math363,Dr._Vaden_ԄGoad,Fall,2001,finalexam,name________________________  Thinkcarefullyandshowallwork,Foldlengthwisewith_test_Ԁinside;putname,rowandseaton  theoutside.  Section1:ThissectioncoversthesamecoursecontentasTest1.Ifyourscoreonthissectionis ` higher,itwillreplacethetest. L   XiXXX1.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyoudiscuss $ t thevarietyofdifferentgeometrymodelsavailableforvariouslimitedsetsofpostulates.  ` 2.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyoudiscuss  8  theincidencepostulatesfromthestandpointofwhatmustbeestablishedinordertouseeach $  postulate.#XiXX Xi#   3.GradethefollowingproofusingA:_correct_Ԁproof,eventhoughitcouldbeclearer(clarifythe   firstunclearstatement)andF:_incorrect_Ԁproof(identifythefirsterror.)   Theorem:Ifxispositiveandyisnegative,thenx2+y2ispositive. p Proof:Sincexispositiveandyisnegative,xyispositive.Thus,sincetheproductoftwo \ positivesispositive,x2y2(whichisequalto(xy)(x+y))ispositive.Since2ispositiveandy2is H positive,2y2ispositive.Finally,sincethesumofpositivesispositive,x2+y2=(x2y2)+(2y2)is 4 positive.  p 4.Statetherulerpostulate.   5.Considerthefollowingsets:S={1,2,3,4_,}_;L={{1,2}_,{_1,4},{1,3},{2,3},{2,4},{3,4}};_P= X  {{1,2,3},{1,3,4}}._ԀIfLrepresentsaproposedletoflinesandPrepresentsaproposedsetof D! planes,whichoftheincidencepostulatesarenotsatisfiedandwhy?(Youdonothavetoreferto 0"  thepostulatesbynumber) #l! 6.StatetheAngleConstructionTheorem (#'   )$( 7.Proveordisprove:Everyangleiscontainedinsomeplane.  8.Proveordisprove:Noangleiscontainedinmorethanoneplane. $  9.Proveordisprove:Everyplaneiscontainedintwolines. 4 10.Proveordisprove:Thereareinfinitelymanyangles. $X"   $D # Name__________________________  Section2:ThissectioncoversthesamecoursecontentasTest2.Ifyourscoreonthissectionis  higher,itwillreplacethetest.   XiXXXi11.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyoudescribe ` howtofindellipsesintaxicabgeometrywhenthefociareneitherhorizontallynorvertically L  orientedtoeachother.(Defineanellipsetobethesetofpointswhosesumofdistancesfromthe 8  fociisafixedconstant.Youcanuseanythingyouknowfrom_coordinate_Ԁgeometry.) $ t 12.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyoudescribe  L  theconnectionsbetweentheparallelpostulateandthevariouspropertiesofatransversaloftwo  8  parallellines.#XiXX Xi # XiXXXi $  #XiXX Xi#13.Statethedefinitionofconvexity:asetisconvexprovided   14.Statethedefinitionofcongruencefortriangles.  \ 15.StatetheSASsimilaritycriterion l 16.Statetheparallelpostulate '#&   |*%) 17.Proveordisprove:If_lines_ԀlandmintersecteachotherandareeachtangenttocirclesCand  D,thentheirpointofintersectioniscollinearwiththecentersofthecircles.  18.Proveordisprove:Thediagonalsofatrapezoidbisecteachother.  8  19.Proveordisprove:Thediagonalsofarectanglearecongruent. H 20.Proveordisprove:Ifthemidpointsoftwosidesofatrianglearejoinedbyalinesegment,the #l! resultingtriangleissimilartotheoriginal. $X"   $D # Name__________________________  Section3:ThissectioncoversthesamecoursecontentasTest3.Ifyourscoreonthissectionis  higher,itwillreplacethetest. h        XiXXXi21.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyoudescribe ` howtoderivethecoordinateequationsforconicsectionsbasedontheirdistanceproperties. L  22.Writeabriefessay(1page:_introduction_,developmentandconclusion)inwhichyou#XiXX Xi7# XiXXXiԀuse $ t coordinatetechniques(andcalculus)todemonstratethatarayemanatingfromthefocusofthe  ` parabola4f(yk)=(xh)2willreflectvertically.  L  #XiXX Xi#23.Supposetheplaneisrotatedcounterclockwise30degreesabouttheorigin.Findtheimageof $  (5,7).   24.Findthepolarcoordinateequationsforatranslationby5inthexdirectionand3inthey \ direction. H 25.Findtheequationoftheellipsewhichresultsiftheellipsewhoseequationis 4 hY 4$ ` \0 `.Eh_is_Ԁrotated30degreescounterclockwise.   26.Findtheequationoftheimageofthelinewhoseequationis2x3y=7underadilationabout $ ! theoriginbyafactorof3. % "   5+&( 27.Supposeyouhavea_sketchpad_Ԁdrawingwhichcontainsapointandaline.Describeindetail  thestepsyouwouldusetoconstructtheparalleltothelinethroughthepoint.  28.Ofallpathsfrom(2,3)totheliney=4andcontinuingonto(5,7),whichistheshortest?   29.Givethematrixformoftheequationsforareflectionaboutthelinex+2y=4.   30.Givethematrixformofthedilationabout_(3,4)_Ԁbyafactorof_1/2_. $D # ́