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TE‐20
SDUHSDMath1Honors
Name: TransformationsandCongruence 6.1HReady,Set,Go!ReadyTopic:PythagoreanTheoremForeachofthefollowingrighttrianglesdeterminethenumberunitmeasureforthemissingside.1.
5
2.
1
3.
√
Topic:FindingdistanceusingPythagoreanTheoremUsethecoordinategridtofindthelengthofeachsideofthetrianglesprovided.4.
5.
TE‐21
SDUHSDMath1Honors
SetTopic:TransformationsTransformpointsasindicatedineachexercisebelow.6. a. RotatepointAaroundtheorigin 90° clockwise,
labelasA’ b. ReflectpointAoverthex‐axis,labelasA”
c. Applytherule 2, 5 ,topointAand
labelA’’’
7. a. ReflectpointBovertheline ,labelasB’
b. RotatepointB180°abouttheorigin,labelasB’’ c. TranslatepointBthepointup3andright7
units,labelasB’’’
TE‐22
SDUHSDMath1Honors
Topic:Slopesofparallelandperpendicularlines.8. Graphalineparalleltothe
givenline.
Equationforgivenline:
Equationfornewline:Answersvary
9. Graphalineperpendicular tothegivenline.
Equationforgivenline:
Equationfornewline:Answersvary
10. Graphalineperpendicular tothegivenline.
Equationforgivenline:
Equationfornewline:Answersvary
GoTopic:GraphinglinearequationsGrapheachequationonthecoordinategridprovided.Extendthelineasfarasthegridwillallow.11. 2 3
12. 2 3
13. Whatsimilaritiesanddifferencearetherebetweentheequationsinnumber11and12?
Samey‐intercept,
oppositeslopes
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SDUHSDMath1Honors
14. 1
15. 3
16. Whatsimilaritiesanddifferencearetherebetweentheequationsinnumber14and15?
Sameslopes,differenty‐
intercepts
Topic:SolveequationsSolveeachequationfortheindicatedvariable.17.3 2 5 8;Solveforx.
18. 3 6 22; Solveforn.
19. 5 2 ;Solveforx.
20. ;Solvefory.
TE‐35
SDUHSDMath1Honors
Name: TransformationsandCongruence 6.2Ready,Set,Go!ReadyTopic:BasicrotationsandreflectionsofobjectsIneachproblemtherewillbeapre‐imageandseveralimagesbasedonthegivenpre‐image.Determinewhichoftheimagesarerotationsofthegivenpre‐imageandwhichofthemarereflectionsofthepre‐image.Ifanimageappearstobecreatedastheresultofarotationandareflectionthenstateboth.1.
Rotation Rotation
Reflection Rotation&Reflection
Pre‐Image ImageA ImageB ImageC ImageD2.
Rotation
Rotation
Rotation&Reflection
Rotation
Pre‐Image ImageA ImageB ImageC ImageDTopic:DefininggeometricshapesandcomponentsForeachofthegeometricwordsbelowwriteadefinitionoftheobjectthataddressestheessentialelements.Also,listnecessaryattributesandcharacteristics.3. Quadrilateral:Foursidedpolygon4. Parallelogram:Quadrilateralwithtwopairsofparallelsides5. Rectangle:Parallelogramwithfourrightangles6. Square:Rectanglewithfourcongruentsides7. Rhombus:Parallelogramwithfourcongruentsides8. Trapezoid:Quadrilateralwithonepairofparallelsides
TE‐36
SDUHSDMath1Honors
SetTopic:ReflectingandrotatingpointsForeachpairofpoint,PandP’,drawinthelineofreflectionthatwouldneedtobeusedtoreflectPontoP’.Thenfindtheequationofthelineofreflection.9.
Equation:
10.
Equation:
Foreachpairofpoint,AandA’,drawinthelineofreflectionthatwouldneedtobeusedtoreflectAontoA’.Thenfindtheequationofthelineofreflection.Also,drawalineconnectingAtoA’andfindtheequationofthisline.ComparetheslopesofthelinesofreflectioncontainingAandA’.11.
EquationoftheLineofReflection:
EquationoftheLine ′:
12.
EquationoftheLineofReflection:
EquationoftheLine ′:
TE‐37
SDUHSDMath1Honors
Topic:ReflectionsandRotations,composingreflectionstocreatearotation13.
a. WhatistheequationforthelineofreflectionthatreflectspointPontoP’?
b.WhatistheequationforthelineofreflectionthatreflectspointP’ontoP’’?
c. CouldP’’alsobeconsideredarotationofpointP?Ifso,whatisthecenterofrotationandhowmanydegreeswaspointProtated?
Yes.Thecentercouldbeanypointonthe
perpendicularbisectorof ′
14.
a. WhatistheequationforthelineofreflectionthatreflectspointPontoP’?
. b.WhatistheequationforthelineofreflectionthatreflectspointP’ontoP’’?
c. CouldP’’alsobeconsideredarotationofpointP?Ifso,whatisthecenterofrotationandhowmanydegreeswaspointProtated?
Yes.Thecentercouldbeanypointontheperpendicularbisectorof ′
TE‐38
SDUHSDMath1Honors
GoTopic:Slopesofparallelandperpendicularlinesandfindingbothdistanceandslopebetweentwopoints.Writetheslopeofalineparalleltothegivenline.15. 7 3 Writetheslopeofalineperpendiculartothegivenline.16. 4 Findtheslopebetweenthegivenpairofpoints.Then,usingthePythagoreanTheorem,findthedistancebetweenthepairofpoints.Youmayusethegraphtohelpyouasneeded.17. 7, 5 2, 7 a. Slope: b. Distance: 13
TE‐39
SDUHSDMath1Honors
Topic:RotationsabouttheoriginPlotthegivencoordinateandthenperformtheindicatedrotationaroundtheorigin,thepoint , ,andplottheimagecreated.Statethecoordinatesoftheimage.
18. Point 4, 2 rotate180° CoordinatesforPoint ,
19. Point 5, 3 rotate 90° CoordinatesforPoint ,
20. Point 7, 3 rotate180° CoordinatesforPoint ,
21. Point 1, 6 rotate 90° CoordinatesforPoint ,
TE‐52
SDUHSDMath1Honors
Name: TransformationsandCongruence 6.3HReady,Set,Go!ReadyTopic:Polygons,definitionandnames1. Whatisapolygon?Describeinyourownwordswhatapolygonis. Answerswillvarybutshouldinclude:closedfigurewithstraightsidesandnocurves.2. Fillinthenamesofeachpolygonbasedonthenumberofsidesthepolygonhas.
NumberofSides NameofPolygon3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon9 Nonagon10 Decagon
Topic:Rotationasatransformation3. Whatfractionofaturndoesthewagonwheel
belowneedtoturninordertoappeartheverysameasitdoesrightnow?Howmanydegreesofrotationwouldthatbe?
4. WhatfractionofaturndoesthemodelofaFerriswheelbelowneedtoturninordertoappeartheverysameasitdoesrightnow?Howmanydegreesofrotationwouldthatbe?
ofaturn; °
ofaturn;20°
TE‐53
SDUHSDMath1Honors
SetTopic:Linesofsymmetryanddiagonals5. Drawthelinesofsymmetryforeachregularpolygon,fillinthetableincludinganexpressionforthe
numberoflinesofsymmetryinan‐sidedpolygon.
NumberofSides
Numberoflinesofsymmetry
3 34 45 56 67 78 8n n
6. Findallofthediagonalsineachregularpolygon.Fillinthetableincludinganexpressionforthenumber
ofdiagonalsinan‐sidedpolygon.NumberofSides
Numberofdiagonals
3 04 25 56 97 148 20n
7. Arealllinesofsymmetryalsodiagonals?Explain. No,somelinesofsymmetrygothroughthemidpointsofoppositesidesoftheregularpolygons
whichmeansthattheselinesofsymmetryarenotdiagonalsofthepolygon.
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SDUHSDMath1Honors
8. Arealldiagonalsalsolinesofsymmetry?Explain. No,onlydiagonalsthatgothroughthecenterofregularpolygonsarelinesofsymmetry.9. Whatshapeswillhavediagonalsthatarenotlinesofsymmetry?Namesomeanddrawthem. Non‐regularpolygons10.Willallparallelogramshavediagonalsthatarelinesofsymmetry?Ifso,drawandexplain.Ifnotdraw
andexplain. Onlysquaresandrhombuseshavediagonalsthatarelinesofsymmetry.Topic: Findinganglesofrotationforregularpolygons.11.Findtheangle(s)ofrotationthatwillcarrythe12sidedpolygonbelowontoitself.
°12.Whataretheanglesofrotation(lessthan360° fora20‐gon?Howmanylinesofsymmetry(linesof
reflection)willithave?
°, °, °, °, °, °, °, °, °, °, °, °, °, °, °, °, °, °, °
20linesofsymmetry13.Whataretheanglesofrotation(lessthan360° fora15‐gon?Howmanylineofsymmetry(linesof
reflection)willithave? °, °, °, °, °, °, °, °, °, °, °, °, °, ° 15linesofsymmetry14.Howmanysidesdoesaregularpolygonhavethathasanangleofrotationequalto18°?Explain. 20sides 20linesofsymmetry15.Howmanysidesdoesaregularpolygonhavethathasanangleofrotationequalto20°?Howmanylines
ofsymmetrywillithave? 18sides 18linesofsymmetry
TE‐55
SDUHSDMath1Honors
GoTopic:Equationsforparallelandperpendicularlines.
FindtheequationofalinePARALLELtothegiveninfoandthroughtheindicatedpoint.
FindtheequationofalinePERPENDICULARtothegivenlineandthroughtheindicatedpoint.
16.Equationofaline:4 1
a. Parallellinethroughpoint1, 7 :
b. Perpendicularlinethoughpoint 1, 7 :
17.Tableofaline: 3 84 10
5 126 14
a. Parallellinethroughpoint3, 8 :
b. Perpendiculartothelinethroughpoint 3, 8 :
18.Graphofaline:
a. Parallellinethroughpoint2, 9 :
b. Perpendicularlinethroughpoint 2, 9 :
TE‐56
SDUHSDMath1Honors
Topic:Reflectingandrotatingpointsonthecoordinateplane.19.ReflectpointAoverthegivenlineofreflectionand
labeltheimageA’.
20. ReflectparallelogramABCDoverthegivenlineofreflectionandlabeltheimageA’B’C’D’.
21. ReflecttriangleABCoverthegivenlineof
reflectionandlabeltheimageA’B’C’.
22. GivenparallelogramQRSTanditsimageQ’R’S’T’drawthelineofreflectionthatwasused.
23. UsingpointPasacenterofrotation.RotatepointQ 120°aboutpointPandlabeltheimageQ’.
24. UsingpointCasthecenterorrotation.RotatepointR270°aboutpointCandlabeltheimageR’.
TE‐64
SDUHSDMath1Honors
Name: TransformationsandCongruence 6.4HReady,Set,Go!ReadyTopic:Definingcongruenceandsimilarity.1. Whatdoyouknowabouttwofiguresiftheyarecongruent? Samesidelengthsandsameanglemeasurements2. Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresarecongruent? Thereisasequenceofrigidmotionsthatmaponeontotheother.3. Whatdoyouknowabouttwofiguresiftheyaresimilar? Sameshape(anglemeasuresarethesame)butdifferentsidelengths.4. Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresaresimilar? Thereisadilationthatmapsoneontotheother.SetTopic:Classifyingquadrilateralsbasedontheirproperties.Usingtheinformationgivendeterminethemostspecificclassificationofthequadrilateral.5. Has180°rotationalsymmetry. 6. Has90°rotationalsymmetry. Parallelogram Square7. Hastwolinesofsymmetrythatarediagonals. 8. Hastwolinesofsymmetrythatarenot
diagonals. Rhombus Rectangle9. Hascongruentdiagonals. 10.Hasdiagonalsthatbisecteachother. Rectangle Parallelogram11.Hasdiagonalsthatareperpendicular. 12.Hascongruentangles. Rhombus Rectangle
TE‐65
SDUHSDMath1Honors
GoTopic:SlopeanddistanceFindtheslopebetweeneachpairofpoints.Then,usingthePythagoreanTheorem,findthedistancebetweeneachpairofpoints.13. 3, 2 0, 0 a. Slope b. Distance: √
14. 7, 1 11, 7 a. Slope b. Distance: 2 √
15. 10, 13 5, 1 a. Slope b. Distance: 13
16. 6, 3 3, 1 a. Slope b. Distance: √
17. 5, 22 17, 28 a. Slope b. Distance: √
18. 1, 7 6, 5 a. Slope b. Distance: 13
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SDUHSDMath1Honors
Topic:SimilarandcongruentfiguresDeterminewhichletterbestdescribestheshapesshown.19.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
20.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
21.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
22.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
23.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
24.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
25.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
26.
a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent
TE‐74
SDUHSDMath1Honors
Name: TransformationsandCongruence 6.5HReady,Set,Go!ReadyTopic:PerformingasequenceoftransformationsThegivenfiguresaretobeusedaspre‐images.Performthestatedtransformationstoobtainanimage.Labelthecorrespondingpartsoftheimageinaccordancewiththepre‐image.1. a. ReflecttriangleABCovertheline
andlabeltheimageA’B’C’. b. RotatetriangleA’B’C’180°aroundthe
originandlabeltheimageA’’B’’C’’.
2. a. ReflectquadrilateralABCDovertheline
2andlabeltheimageA’B’C’D’. b. RotatethequadrilateralA’B’C’D’90°
around 2, 3 .LabeltheimageA’’B’’C’’D’’.
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SDUHSDMath1Honors
Topic:Findthesequenceoftransformations.Findthesequenceoftransformationsthatwillcarry∆ onto∆ ’ ’ ’.Clearlydescribethesequenceoftransformationsbeloweachgrid.3. 4.
Translate8unitsup,rotate ° Translate8unitsleft,reflectover . aboutpointT,andreflectabout .SetTopic:TrianglecongruenciesExplainwhetherornotthetrianglesarecongruent,similar,orneitherbasedonthemarkingsthatindicatecongruence.5.
Congruent
6.
Similar
7.
Neither
8.
Congruent
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SDUHSDMath1Honors
9.
Congruent
10.
Neither
Usethegivencongruencestatementtodrawandlabeltwotrianglesthathavethepropercorrespondingpartscongruenttooneanother.11.∆ABC ≅ ∆PQR
12. ∆ ≅ ∆
GoTopic:Graphingfunctionsandmakingcomparisons.Grapheachpairoffunctionsandmakeanobservationabouthowthefunctionscomparetooneanother.13. 2
2
Thelineshavethesamey‐intercept
14. 2 2
Thecurvesarereflectionsoverthex‐axis.
TE‐77
SDUHSDMath1Honors
Topic:ReviewoffindingrecursiverulesforsequencesUsethegivensequenceofnumberstowritearecursiveruleforthenthvalueofthesequence.15.3, 6, 12, 24, … , ⋅
16. , 0, , 1, … ,
Topic:TrianglecongruencepropertiesQuestions#17‐20canbecompletedbygoingto:http://illuminations.nctm.org/Activity.aspx?id=3504Investigatecongruencebymanipulatingtheparts(sidesandangles)ofatriangle.Ifyoucancreatetwodifferenttriangleswiththesameparts,thenthosepartsdonotprovecongruence.Canyouproveallthetheorems(SAS,,SSA,SSS,AAS,ASA,AAA)?17.Eachtrianglecongruencetheoremusesthreeelements(sidesandangles)toprovecongruence.Select
threetriangleelementsfromthetop,rightmenutostart.(Note:Thetooldoesnotallowyoutoselectmorethanthreeelements.Ifyouselectthewrongelement,simplyunselectitbeforechoosinganotherelement.)Thiscreatesthoseelementsintheworkarea.
Onthetopofthetoolbar,thethreeelementsarelistedinorder.Forexample,ifyouchoosesideAB,angleA,andangleB,youwillbeworkingonAngle–Side–Angle.IfinsteadyouchoosesideAB,angleA,andangleC,youwillbeworkingonAngle–Angle–Side.Thetwotheoremsaredifferent,eventhoughbothinvolvetwoanglesandoneside.
18.Constructyourtriangle:
Movetheelementsofthetrianglesothatpointslabeledwiththesamelettertouch. Clickanddragadottomovetheelementtoanewlocation. Clickanddragaside'sendpointorangle'sarrowtorotatetheelement.Thecenterofrotationisthe
side'smidpointortheangle'svertex,respectively. Tohelpplaceelements,pointsmarkedwiththesamelettersnaptogether.Whenanglessnap,the
raysareextendedtotheedgeoftheworkarea. Whenyoucreateaclosedtriangle,thepointsmergeandcenterisfilledin. Onceatriangleisformedwiththeoriginalthreeelements,thetrianglemovestothebottom,right
corneroftheworkarea,andcongruentelementsappear.
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SDUHSDMath1Honors
Name: TransformationsandCongruence 6.6HReady,Set,Go!ReadyTopic:CorrespondingpartsoffiguresandtransformationsGiventhefiguresineachsketchwithcongruentanglesandsidesmarked,firstlistthepartsofthefiguresthatcorrespond(Forexample,in#3,∠ ≅ ∠ ).Thendetermineifareflectionoccurredaspartofthesequenceoftransformationsthatwasusedtocreatetheimage.1.
Congruencies∠ ≅ ∠
≅ ≅
Reflected?YesorNo
2.
Congruencies≅ ≅
∠ ≅ ∠ ∠ ≅ ∠ ∠ ≅ ∠ ∠ ≅ ∠
Reflected?YesorNo
TE‐88
SDUHSDMath1Honors
SetTopic:Usecongruenttrianglecriteriaandtransformationstojustifyconjectures.Ineachproblembelowtherearesometruestatementslisted.Fromthesestatementsaconjecture(aguess)aboutwhatmightbetruehasbeenmade.Usingthegivenstatementsandconjecturestatementcreateanargumentthatjustifiestheconjecture.3. Truestatements: PointMisthemidpointof ∠ ≅ ∠ ≅
Conjecture: ∠ ≅ ∠a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: ThetwotrianglesarecongruentbySAS.Therefore,the
correspondingpartsarecongruent.
4. Truestatements: ∠ ≅ ∠ ≅
Conjecture: bisects∠ a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: ThetwotrianglesarecongruentbySAS.Therefore,
correspondingpartsarecongruentsince∠ ≅ ∠ and bisects∠
5. Truestatements: ∆ isa180°rotationof ∆
Conjecture: ∆ ≅ ∆a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: Arotationmaps∆ only .Therefore,∆ ≅ ∆ ,
≅ , ≅ .∠ ≅ ∠ because∠ ≅∠ andtheyare2linearpairs∠ &∠ and∠ &∠ .Therefore,thetrianglesarecongruentbySAS.
TE‐89
SDUHSDMath1Honors
GoTopic:Createbothexplicitandrecursiverulesforthevisualpatterns.6. Findanexplicitfunctionruleandarecursiverulefordotsinstepn.
Step1 Step2 Step3 Explicit: Recursive: , 7. Findanexplicitfunctionruleandarecursiveruleforsquaresinstepn.
Explicit: Recursive: , Findanexplicitfunctionruleandarecursiveruleforthevaluesineachtable.8.
Step Value1 12 113 214 31
Explicit: Recursive: ,
9.
2 163 84 45 2
Explicit:
Recursive:
⋅
10. 1 52 253 1254 625
Explicit: Recursive:
⋅
Topic:Reviewofsolvingequations.Solveeachequationfort.11. 13
12. 10 4 12 3
TE‐98
SDUHSDMath1Honors
Name: Constructions 6.7HReady,Set,Go!ReadyTopic:TransformationsoflinesForeachsetoflinesusethepointsonthelinetodeterminewhichlineistheimageandwhichisthepre‐image,labelthem,writeimagebytheimagelineandpreimagebytheoriginalline.Thendefinethetransformationthatwasusedtocreatetheimage.Finallyfindtheequationforeachline.1.
a. DescriptionofTransformation:
translated4unitsupb. Equationforpre‐image:
c. Equationforimage:
2.
a. DescriptionofTransformation:
Reflectabout b. Equationforpre‐image:
c. Equationforimage:
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SDUHSDMath1Honors
SetTopic: Trianglecongruenceproperties3. Truestatements: ∠ ≅ ∠ ∠ ≅ ∠ ≅
Conjecture: ≅ a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: ThetrianglesarecongruentASA.Therefore, ≅ because
theyarecorrespondingpartsofcongruenttriangles.
4. Truestatements: ∠ ≅ ∠ ≅
Conjecture: bisects∠ a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: ThetrianglesarecongruentbySAS.Therefore,∠ ≅ ∠
becausetheyarecorrespondingpartsofcongruenttriangles.
5. Truestatements: Wisthemidpointof ≅
Conjecture: isperpendicularto a. Istheconjecturecorrect?Yesb. Argumenttoproveyouareright: ThetrianglesarecongruentbySSS.Therefore,∠ ≅ ∠
becausetheyarecorrespondingpartsofcongruenttriangles.Theyare °togetherand °each.
TE‐100
SDUHSDMath1Honors
Topic:Geometricconstructions6. Accordingtotheconstructionshowninthediagramtotheright,
whatdowecallsegment ? Altitudeof∆ fromBto 7. Whatdotheconstructionmarksinthefigurebelowcreate?
Perpendicularbisectorof 8. Whichdiagramshowstheconstructionofanequilateraltriangle?
a. b. c. d. GoTopic:SolvingsystemsofequationsSolveeachsystemofequations.Utilizesubstitutionorelimination.
9.11
2 19
,
10.4 9 9
3 6
,
11.2 114 2
,
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SDUHSDMath1Honors
Name: Constructions 6.8HReady,Set,Go!ReadyTopic:Transformationsoflines,algebraicandgeometricthoughts.Foreachsetoflinesusethepointsonthelinetodeterminewhichlineistheimageandwhichisthepre‐image,labelthem,writeimagebytheimagelineandpreimagebytheoriginalline.Thendefinethetransformationthatwasusedtocreatetheimage.Finallyfindtheequationforeachline.1.
a. DescriptionofTransformation:
Translateleft7
b. Equationforpre‐image:
c. Equationforimage:
2.
a. DescriptionofTransformation:
Rotate °aboutP
b. Equationforpre‐image:
c. Equationforimage:
TE‐110
SDUHSDMath1Honors
SetTopic:Transformationsandtrianglecongruence.Determinewhetherornotthestatementistrueorfalse.Iftrue,explainwhy.Iffalse,explainwhynotorprovideacounterexample.3. Ifonetrianglecanbetransformedsothatoneofitsanglesandoneofitssidescoincidewithanother
triangle’sangleandsidethenthetwotrianglesarecongruent. False.ThereisapossibilityofhavingaSSAsituation.4. Ifonetrianglecanbetransformedsothattwoofitssidesandanyoneofitsangleswillcoincidewithtwo
sidesandananglefromanothertrianglethenthetwotriangleswillbecongruent. False.ThereisapossibilityofhavingaSSAsituation.5. Ifthreeanglesofonetrianglearecongruenttothreeanglesofanothertriangle,thenthereisasequence
oftransformationsthatwilltransformonetriangleontotheother. False.Thetrianglesmaybesimilarorcongruent.6. Ifthreesidesofonetrianglearecongruenttothreesidesofanothertriangle,thenthereisasequenceof
transformationsthatwilltransformonetriangleontotheother. True.SSSisoneofthetrianglecongruencies.7. Foranytwocongruentpolygonsthereisasequenceoftransformationsthatwilltransformoneofthe
polygonsontotheother. True.Ifthepolygonsarecongruent,theycanberotated,reflected,and/ortranslatedtotransform
oneontotheother.Topic:Geometricconstructions8. Whenfinishedwiththeconstructionfor“CopyanAngle”,segmentsaredrawnconnectingwherethearcs
crossthesidesoftheangles.Whatmethodprovesthesetwotrianglestobecongruent?
a. ASA b.SAS c.SSS d.AAS
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SDUHSDMath1Honors
9. Whichillustrationshowsthecorrectconstructionofananglebisector?
a. b. c. d. GoTopic:Trianglecongruenceandpropertiesofpolygons.10.Whatistheminimumamountofinformationneededtodeterminethattwotrianglesarecongruent?List
allpossiblecombinationsofneededcriteria. 3piecesofinformation(anglesand/orsides)areneededtodeterminethattwotrianglesare
congruent. Possiblecombinationsofneededcriteria:SSS,ASA,SAS,AAS11.Whatisalineofsymmetryandwhatisadiagonal?Aretheythesamething?Couldtheybethesameina
polygon?Ifsogiveanexample,ifnotexplainwhynot.
Alineofsymmetrycutsthediagonalintotwocongruentshapesthataremirrorimagesofeachother.
Adiagonalconnectstwonon‐adjacentvertices12.Howisthenumberoflinesofsymmetryforaregularpolygonconnectedtothenumberofsidesofthe
polygon?Howisthenumberofdiagonalsforapolygonconnectedtothenumberofsides? Thenumberoflinesofsymmetryforaregularpolygonisthesameasthenumberofsidesofthe
polygon.
Thenumberofdiagonalsisequationto wherenisthenumberofsides.13.Whatdorighttriangleshavetodowithfindingdistancebetweenpointsonacoordinategrid?
ThePythagoreanTheoremcanbeusedtofindthedistancebetweenpointsonthecoordinategrid.
TE‐112
SDUHSDMath1Honors
Topic:Findingdistanceandslope.Foreachpairofgivencoordinatepointsfinddistancebetweenthemandfindtheslopeofthelinethatpassesthroughthem.Showallyourwork.14. 10, 31 20, 11
a. Slope: b. Distance: √
15. 16, 45 34, 75
a. Slope: b. Distance: 130
16. 8, 21 20, 11
a. Slope: b. Distance: √
17. 10, 0 14, 18
a. Slope: b. Distance: 30
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SDUHSDMath1Honors
Module6ReviewHomework1. Describethesequenceofrigidmotionsthatshows∆ ≅ ∆ .
Reflectoverthex‐axisandthentranslateright4units.
2. Usethecoordinategrid,below,tocompleteparts(a)–(c).
a. Reflect∆ acrosstheverticalline,paralleltothe ‐axis,goingthroughpoint 1, 0 .Labelthetransformedpoints as , , ,respectively.SeeimageinREDbelow.
b. Reflect∆ acrossthehorizontalline,paralleltothe ‐axisgoingthroughpoint 0, 1 .Labelthetransformedpointsof ’ ’ ’as ,respectively.SeeimageinBLUEbelow.
c. Describeasinglerigidmotionthatwouldmap∆ to∆ .Rotation °abouttheorigin.
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SDUHSDMath1Honors
3. Pre‐image: 0, 0 , 5, 1 , 5, 4 a. Rotatethefigure 90°abouttheorigin.Labelthe
imageas ′ ′ ′.SeeimageinRED.
b. Reflect ′ ′ ′overthey‐axis.Labeltheimageas′′ ′′ ′′.SeeimageinBLUE.
c. Translate ′′ ′′ ′′right3unitsanddown1unit.Labeltheimageas ′′′ ′′′ ′′′.SeeimageinGREEN.
4. Pre‐image: 1, 2 , 1, 5 , 4, 4 a. Translatethefigureup2unitsandleft5units.
Labeltheimageas ′ ′ ′.SeeimageinRED.
b. Reflect ′ ′ ′overthex‐axis.Labeltheimageas′′ ′′ ′′.SeeimageinBLUE.
c. Rotate ′′ ′′ ′′180°abouttheorigin.Labeltheimageas ′′′ ′′′ ′′′.SeeimageinGREEN.
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SDUHSDMath1Honors
5. Pre‐image: 3, 1 , 2, 1 , 2, 2 Performthefollowingsequenceoftransformations:Reflecttheimageoverthegivenline(lineL),thenrotate180°aroundtheorigin,thentranslateup5units.
Topic:Rotationsymmetryforregularpolygonsandtransformations6. Whatanglesofrotationalsymmetryarethereforaregularpentagon? 72°,144°,216°,288°,360°7. Whatanglesofrotationalsymmetryarethereforaregularhexagon? 60°,120°,180°,240°,300°,360°8. Ifaregularpolygonhasanangleofrotationalsymmetrythatis40°,howmanysidesdoesthepolygon
have? 9sides
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SDUHSDMath1Honors
Oneachgivencoordinategridbelowperformtheindicatedtransformation.9. ReflectpointPoverlinej.
10. RotateP 90° aroundpointC.
Topic:Connectingtableswithtransformations.Foreachfunctionfindtheoutputsthatfillinthetable.Thendescribetherelationshipbetweentheoutputsineachtable.11. 2
1 22 43 64 8
2 3123 04 2
12. 4
1 42 163 644 256
4
1
2
3 1
4 4
Relationshipbetween and :isalways6lessthan
Relationshipbetweent(x)andh(x):isalways3stepsbehind
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SDUHSDMath1Honors
Ineachfigurefindandmarkatleastfourpossiblecentersofrotationthatwouldworkforrotatingthepre‐imagepointtotheimagepoint.13.
Centersofrotation: Answersmayvary.Anypointonthelines .
14.
Centersofrotation: Answersmayvary.Anypointontheline .
Findthepointofrotationthatmapseachpre‐imagetotheimage.15.
,
16.
,
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SDUHSDMath1Honors
Findthelineofreflectionthatmapseachpre‐imagetotheimage.17.
18.
Topic:Constructingregularpolygonsinscribedinacircle19.Constructanisoscelestrianglethatincorporates asoneofthesides.Constructthecirclethat
circumscribesthetriangle.
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SDUHSDMath1Honors
20.Constructahexagonthatincorporates asoneofthesides.Constructthecirclethatcircumscribesthehexagon.
21.Constructasquarethatincorporates asoneofthesides.Constructthecirclethatcircumscribesthat
square.
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SDUHSDMath1Honors
IntrotoModule7Honors‐GotheDistanceADevelopUnderstandingTaskTheperformancesofthePodunkHighSchooldrillteamareverypopularduringhalf‐timeattheschool’sfootballandbasketballgames.WhenthePodunkHighSchooldrillteamchoreographsthedancemovesthattheywilldoonthefootballfield,theylayouttheirpositionsonagridliketheonebelow:
Inoneoftheirdances,theyplantomakepatternsholdinglong,wideribbonsthatwillspanfromonedancerinthemiddletosixotherdancers.Onthegrid,theirpatternlookslikethis:
Thequestionthedancershaveishowlongtomaketheribbons.SomedancersthinkthattheribbonfromGene(G)toCasey(C)willbeshorterthantheonefromGene(G)toBailey(B).1. Howlongdoeseachribbonneedtobe? EachRibbonneedstobe5unitslong2. Explainhowyoufoundthelengthofeachribbon. UsePythagoreanTheoremforeachribbon,exceptforGFandGC.
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SDUHSDMath1Honors
Whentheyhavefinishedwiththeribbonsinthisposition,theyareconsideringusingthemtoformanewpatternlikethis:
3. WilltheribbonstheyusedinthepreviouspatternbelongenoughtogobetweenBailey(B)andCasey(C)inthenewpattern?Explainyouranswer.
Yes,becausetheywillonlyneed√ √ units,whichislessthan5.
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SDUHSDMath1Honors
Genenoticesthatthecalculationssheismakingforthelengthoftheribbonsremindsherofmathclass.Shesaystothegroup,“Hey,Iwonderifthereisaprocessthatwecoulduselikewhatwehavebeendoingtofindthedistancebetweenanytwopointsonthegrid.”Shedecidestothinkaboutitlikethis:“I’mgoingtostartwithtwopointsanddrawthelinebetweenthemthatrepresentsthedistancethatI’mlookingfor.Sincethesetwopointscouldbeanywhere,InamedthemA , andB , .Hmmmm....whenIfiguredthelengthoftheribbons,whatdidIdonext?”
4. Thinkbackontheprocessyouusedtofindthelengthoftheribbonandwritedownyourstepshere,usingpointsAandB.
5. Usetheprocessyoucameupwithinquestion4tofindthedistancebetweentwopointslocatedat
1, 5 and 2, 6 √ 6. Useyourprocesstofindtheperimeterofthehexagonpatternshownabovequestion3. √
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SDUHSDMath1Honors
IntrotoModule7Honors‐Ready,Set,Go!ReadyTopic:FindingthedistancebetweentwopointsUsethenumberlinetofindthedistancebetweenthegivenpoints.(Note:ThenotationABmeansthedistancebetweenpointsAandB.)1. AE 2. GB 3. BF 6 7.5 6
4. Describeawaytofindthedistancebetweentwopointsonanumberlinewithoutcountingthespaces. FindtheabsolutevalueofthedifferencebetweenthepointsTopic:Graphinglines.Thegraphattherightisoftheline .5. Onthesamegrid,graphaparallellinethatis4unitsbelowit. Dashedlineatright6. Writetheequationofthenewline. 7. Writethey‐interceptofthenewlineasanorderedpair. , 8. Writethex‐interceptasanorderedpair. , 9. a. Writetheequationofthenewlineinpoint‐slopeform
usingthey‐intercept b. Writetheequationofthenewlineinpoint‐slopeformusingthex‐intercept. c. Explaininwhatwaytheequationsin5aand5barethesameandinwhatwaytheyaredifferent.
Simplifiedequationsareequivalent.Differenceisinthestartingpoint.
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SDUHSDMath1Honors
SetTopic:Slopetrianglesandthedistanceformula.∆ isaslopetrianglefor whereBCistheriseandACistherun.Noticethatthelengthof hasacorrespondinglengthonthey‐axisandthelengthof hasacorrespondinglengthonthex‐axis.Theslopeformulaiswrittenas wheremistheslope.
10. a. Whatdoesthevalue tellyou?
theverticaldistance
b. Whatdoesthevalue tellyou?
thehorizontaldistance InthepreviousmoduleyoufoundthelengthofaslantedlinesegmentbydrawingtheslopetriangleandperformingthePythagoreanTheorem.Inthisexercisetrytodevelopamoreefficientmethodoffindingthelengthofalinesegmentbyusingthemeaningof and combinedwiththePythagoreanTheorem.11. FindAB
√ .
12. FindAB
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SDUHSDMath1Honors
GoTopic:RectangularcoordinatesUsethegiveninformationtofillinthemissingcoordinates.Thenfindthelengthoftheindicatedlinesegment.
Coordinatesongraphsareintentionallyleftblank13. a. FindHB
20 b. FindBD
10
Topic:Writingequationsoflines.Writetheequationofthelineinpoint‐slopeformusingthegiveninformation.14. Slope= point(12,5)
15. 11, 3 , 6, 2
16. x‐intercept: 2,y‐intercept:‐3
17. Allx valuesare‐7,y canbeanything
18. Slope: ,x‐intercept:5
19. 10,17 , 13, 17
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SDUHSDMath1Honors
EndofModule6HonorsChallengeProblemsThefollowingproblemsareintendedforstudentstoworkonafterModule6HTest.Theproblemsfocusonusingsimilartrianglestofindarea.ThenextmodulebuildsontheideaofconnectingAlgebraandGeometry.Thefollowingpageisblankfortheteachertocopyandgivetoeachstudentafterthetest.Belowarethesolutions.BothrighttriangleABCandisoscelestriangleBCD,shownhere,haveheight5cmfrombase 12cm.Usethefigureandinformationprovidedtoanswerthefollowingquestions.
1. WhatistheabsolutedifferencebetweentheareasofΔABCandΔBCD?
TheareasofΔABCandΔBCDcanbedenotedby[ΔABC]and[ΔBCD],respectively.Thisnotationwillbeusedtodenotetheareasofthetrianglesthroughoutthissolutionset.SinceΔABCandΔBCDbothhavebase cmandheight5cm,itfollowsthat .Therefore,becausethetwotriangleshavethesamearea,theabsolutedifferenceintheareasis
.2. WhatistheratiooftheareaofΔABEtoΔCDE?
Fromthefigure,weseethat .Similarly, .Again,since ,wecanwritethefollowingequation:
.Whensimplified,wehave ,sotheratio .
3. WhatistheareaofΔBCE?
ThefigureshowsaltitudeEYofΔBCEandaltitudeDXofΔBCD,bothdrawnperpendiculartobaseBC.Noticethat ~ ,whichmeansthelengthsofcorrespondingsidesareproportionate.
Also,noticethat ~ .Itfollows,then,that cm2.
4. WhatistheareaofpentagonABCDE?
Therefore,theareaofpentagonABCDEis – – – cm2.