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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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.