GeometryUnit7ProportionsandSimilarity
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Date LessonName DaysSuggested
GetReadyforChapter7TE490 1
7.1Dilations 2
7.2SimilarPolygons 1
7.3SimilarTrianglesAASimilarity 1.5
7.4SimilarTrianglesSSSandSASSimilarity 1.5
Quiz 0.5
7.5ParallelLinesandProportionalParts 1
7.6PartsofSimilarTriangles 1.5
Review 1
Test 1
Total 12
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GetReadyforChapter7
GuidedPractice
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7.1Dilations
Example1UsearulertodrawtheimageoftrapezoidPQRSunderadilationwithcenterCandascalefactorof3.GuidedPractice1Whichdiagramshowsthedilationimageof∆𝐿𝑀𝑁withcenterCand𝑘 = !
!?
a. b.
c. d.
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Example2PUPPETSTocreatetheillusionofa“life-sized”image,puppeteerssometimesandusealightsourcetoshowanenlargedimageofapuppetprojectedonascreenorwall.SupposethatthedistancebetweenalightsourceLandthepuppetis24inches(LP).TowhatdistancePP’shouldyouplacethepuppetfromthescreentocreatea49.5-inchtallshadow(I’M’)froma9-inchpuppet?
GuidedPractice2PUPPETSSupposeyouhaveasimilarsituationwiththepuppetandalightsource.ThedistancebetweenthelightsourceLandthepuppetis30inches(LP).Towhatdistanceshouldyouplacethepuppetfromthescreentocreatea54-inchtallshadow(I’M’)froma6-inchpuppet?
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Example3Graphtheimageofeachpolygonwiththegivenverticesafteradilationattheindicatedcenterwiththegivenscalefactor.A. B.𝐸 −8, 4 , 𝐹 −4, 8 , 𝐺 8, 4 , 𝐴 −2,−4 , 𝐵 3, 2 , 𝐶 (0, 4);origin;𝑎𝑛𝑑 𝐻 −4,−8 ; origin;𝑘 = !
! 𝑘 = 1.5
GuidedPractice3TriangleABChasvertices𝐴 −1, 1 , 𝐵 2,−2 ,and 𝐶 (−1,−2).Findtheimageof∆ABCafteradilationcenteredattheoriginwithascalefactorof2.Sketchthepreimageandtheimage.
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ExtraPractice7.11.Quadrilateral𝐽𝐾𝐿𝑀hasthevertices𝐽(−2, 4),𝐾(−2,−2),𝐿 −4,−2 ,and𝑀(−4, 2).Graphtheimageof𝐽𝐾𝐿𝑀afterdilationcenteredattheoriginwithascalefactorof2.5. 2.Trapezoid𝐸𝐹𝐺𝐻hasvertices𝐸(−8, 4),𝐹(−4, 8),𝐺(8, 4),and𝐻(−4,−8).Graphtheimage𝐸𝐹𝐺𝐻after
dialationcenteredattheoriginwithscalefactorof!!.
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7.2SimilarPolygonsExample1Determinewhetherthegivenpolygonsaresimilar.Explain.A.ABCDandEFGH B.∆PQRand∆STU
Example2If∆ABC~∆RST,listallpairsofcongruentanglesandwriteaproportionthatrelatesthecorrespondingsides.
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Example3MENUSTanisdesigninganewmenufortherestaurantwhereheworks.Determinewhetherthefollowingsizesforthenewmenuaresimilartotheoriginalmenu.Ifso,writethesimilaritystatementandscalefactor.Explainyourreasoning.
A. B.
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Example4Thetwopolygonsaresimilar.
A. Findx.
B. Findy.GuidedPractice4Thetwopolygonsaresimilar.Findx.
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Example5IfABCDE~RSTUV,findthescalefactorofRSTUVtoABCDEandtheperimeterofeachpolygon.
GuidedPractice5IfABCDE~PQRST,findthescalefactorofABSDEtoPQRSTandtheperimeterofeachpolygon.
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ExtraPractice7.21.Determinewhethereachpairoffiguresissimilar.Ifso,writethesimilaritystatementandscalefactor.Ifnotexplainyourreasoning.
2.
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7.3SimilarTrianglesAASimilarity
Example1Determinewhetherthetrianglesaresimilar.Ifso,writeasimilaritystatement.Explainyourreasoning.A. B.
Example2∆QRSand∆WXYareisoscelestriangles.Whichofthefollowingisanincorrectstatement?Whichofthefollowingwouldnotbesufficienttoprovethat∆QRS~∆WXY?A.ΔQRS≅ΔWXYB.∠QRS≅∠WXYC.∠QRSand∠WXYarethevertexanglesand∠QRS≅∠WXY.D.∠QRSand∠WXYarebaseanglesand∠QRS≅∠WXY.
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Example3 GuidedPractice3ALGEBRAGiven𝑅𝑆 || 𝑈𝑇,𝑅𝑆 = 4, FindWRandWT.𝑅𝑄 = 𝑥 + 3,𝑄𝑇 = 2𝑥 + 10,𝑈𝑇 = 10. FindRQandQT. Example4 GuidedPractice4SKYSCRAPERSJoshwantedtomeasuretheheightoftheWillisTowerinChicago.Heuseda12-footlightpoleandmeasureditsshadowat1:00PM.Thelengthoftheshadowwas2feet.ThenhemeasuredthelengthoftheWillisTower’sshadowanditwas242feetatthesametime.WhatistheheightoftheWillisTower?
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7.4SimilarTrianglesSSSandSASSimilarity
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Example1Determinewhetherthetrianglesaresimilar.Ifso,writeasimilaritystatement.Explainyourreasoning.A. B.
Example2DeterminewhetherrDEFwithverticesD(–4,0),E(6,–1),andF(3,3)issimilartorLMNwithverticesL(–3,–5),M(15,–7),andN(11,–1).Explainyourreasoning.
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Example3Determinewhetherthetrianglesaresimilar.Ifso,writeasimilaritystatement.Explainyourreasoning.A. B. Example4DeterminewhetherrABCwithverticesA(–2,7),B(–2,–8),andC(4,4)issimilartorDECwithverticesD(0,6)andE(0,–4).Explainyourreasoning.
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Example5Joaquinwantstomeasuretheheightofabuildingobstructinghisviewofthelake.Hestandssothatthetipofhisshadowcoincideswiththetipofthebuilding’sshadow.Heis5feet6inchestall,andhisshadowis18feetlongatthesametimethatthebuilding’sshadowis360feetlong.Abouthowtallisthebuilding?
GuidedPractice5Connorisstandingnexttotheflagpoleathisschoolandwantstousehisshadowtohelpmeasurethepole.Connoris5feet9inchestallandthelengthofhisshadowis8feetwhentheflagpole’sshadowis50feet.Howhighistheflagpoletothenearestfoot?
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ExtraPractice7.3-7.4
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7.5ParallelLinesandProportionalParts
Example1 GuidedPractice1IntriangleRST,RTisparalleltoVU, IntriangleABC,ACisparalleltoXY,AX=4,SV=3,VR=8,andUT=12.FindSU. XB=10.5,andCY=6.FindBY.
Example2 GuidedPractice2IntriangleDEF,DH=18,HE=36,andDG=!
!GF. IntriangleWXZ,XY=15,YZ=25,WA=18,and
DeterminewhetherGHandFEareparallel. AZ=32.DeterminewhetherWXandAYparallel.
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Example3Inthefigure,DEandEFaremidsegmentsofΔABC.
A. FindAB.
B. FindFE.
C. Findm∠AFE.GuidedPractice3Inthefigure,DEandDFaremidsegmentsofΔABC.FindBC.
A. FindBC.
B. FindDE.
C. Findm∠AFD.
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Example4MAPSInthefigure,Larch,Maple,andNuthatchStreetsareallparallel.Thefigureshowsthedistancesinbetweencityblocks.Findx.
GuidedPractice4Inthefigure,Davis,Broad,andMainStreetsareallparallel.Thefigureshowsthedistancesinbetweencityblocks.Findx.
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Example5ALGEBRAFindxandy.
GuidedPractice5Findaandb.
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7.6PartsofSimilarTriangles
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Example1 GuidedPractice1Inthefigure,ΔLJK~ΔSQR.Findthe Inthefigure,ΔABC~ΔFGH.Findthevalueofx.valueofx.
Example2ESTIMATINGDISTANCESanjay’sarmisabout9timeslongerthanthedistancebetweenhiseyes.Hesightsastatueacrosstheparkthatis10feetwide.Ifthestatueappearstomove4widthswhenheswitcheseyes,estimatethedistancefromSanjay’sthumbtothestatue.
GuidedPractice2UsetheinformationfromExample2.SupposeSanjayturnsaroundandseesasailboatinthelakethatis12feetwide.Ifthesailboatappearstomove4widthswhenheswitcheseyes,estimatethedistancefromSanjay’sthumbtothesailboat.
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Example3 GuidedPractice3Findx. Findn.
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ExtraPractice7.6Findx.1. 2.3. 4.