transformations and congruence 6.1h set,...

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.



10. Graphalineperpendicular tothegivenline.



GoTopic:GraphinglinearequationsGrapheachequationonthecoordinategridprovided.Extendthelineasfarasthegridwillallow.11. 2 3

12. 2 3

13. Whatsimilaritiesanddifferencearetherebetweentheequationsinnumber11and12?

Samey‐intercept,

oppositeslopes

TE‐23

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.

TE‐54

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


b. Perpendiculartothelinethroughpoint 3, 8 :

18.Graphofaline:


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

TE‐66

SDUHSDMath1Honors

Topic:SimilarandcongruentfiguresDeterminewhichletterbestdescribestheshapesshown.19.

a. Theshapesareonlycongruentb. Theshapesareonlysimilarc. Theshapesarebothsimilarandcongruentd. Theshapesareneithersimilarnorcongruent

20.


21.


22.


23.


24.


25.


26.


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’’.

TE‐75

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

TE‐76

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.

TE‐87

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.


Reflectabout b. Equationforpre‐image:


TE‐99

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

,

TE‐101

SDUHSDMath1Honors

12.1

2 1

,

13.2 7

3 8

,

14.4 76 2 8

,

TE‐109

SDUHSDMath1Honors

Name: Constructions 6.8HReady,Set,Go!ReadyTopic:Transformationsoflines,algebraicandgeometricthoughts.Foreachsetoflinesusethepointsonthelinetodeterminewhichlineistheimageandwhichisthepre‐image,labelthem,writeimagebytheimagelineandpreimagebytheoriginalline.Thendefinethetransformationthatwasusedtocreatetheimage.Finallyfindtheequationforeachline.1.


Translateleft7

b. Equationforpre‐image:


2.


Rotate °aboutP

b. Equationforpre‐image:


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

TE‐111

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

TE‐127

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.

TE‐128

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.

TE‐129

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

TE‐130

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

TE‐131

SDUHSDMath1Honors

Ineachfigurefindandmarkatleastfourpossiblecentersofrotationthatwouldworkforrotatingthepre‐imagepointtotheimagepoint.13.

Centersofrotation: Answersmayvary.Anypointonthelines .

14.

Centersofrotation: Answersmayvary.Anypointontheline .

Findthepointofrotationthatmapseachpre‐imagetotheimage.15.

,

16.

,

TE‐132

SDUHSDMath1Honors

Findthelineofreflectionthatmapseachpre‐imagetotheimage.17.

18.

Topic:Constructingregularpolygonsinscribedinacircle19.Constructanisoscelestrianglethatincorporates asoneofthesides.Constructthecirclethat

circumscribesthetriangle.

TE‐133

SDUHSDMath1Honors

20.Constructahexagonthatincorporates asoneofthesides.Constructthecirclethatcircumscribesthehexagon.

21.Constructasquarethatincorporates asoneofthesides.Constructthecirclethatcircumscribesthat

square.

TE‐134

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.

TE‐135

SDUHSDMath1Honors

Whentheyhavefinishedwiththeribbonsinthisposition,theyareconsideringusingthemtoformanewpatternlikethis:

3. WilltheribbonstheyusedinthepreviouspatternbelongenoughtogobetweenBailey(B)andCasey(C)inthenewpattern?Explainyouranswer.

Yes,becausetheywillonlyneed√ √ units,whichislessthan5.

TE‐136

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. √

TE‐137

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.

TE‐138

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

TE‐139

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

TE‐140

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.

transformations and congruence 6.1h set,...

Documents