TE‐20 Name:
TransformationsandCongruence 6.1H
Ready,Set,Go!
Ready
Topic:PythagoreanTheorem
Foreachofthefollowingrighttrianglesdeterminethenumberunitmeasureforthemissingside.
1.
2.
3.
1
5
√
Topic:FindingdistanceusingPythagoreanTheorem
Usethecoordinategridtofindthelengthofeachsideofthetrianglesprovided.
4.
5.
SDUHSDMath1Honors
TE‐21 Set
Topic:Transformations
Transformpointsasindicatedineachexercisebelow.
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’’’
SDUHSDMath1Honors
TE‐22 Topic:Slopesofparallelandperpendicularlines.
8. Graphalineparalleltothe
9. Graphalineperpendicular to
givenline.
thegivenline.
Equationforgivenline:
Equationfornewline:
Answersvary
Equationforgivenline:
Equationfornewline:
Answersvary
10. Graphalineperpendicular to
thegivenline.
Equationforgivenline:
Equationfornewline:
Answersvary
Go
Topic:Graphinglinearequations
Grapheachequationonthecoordinategridprovided.Extendthelineasfarasthegridwillallow.
11.
2
3
12. 2
3
13. Whatsimilaritiesand
differencearethere
betweentheequationsin
number11and12?
Samey‐intercept,
oppositeslopes
SDUHSDMath1Honors
TE‐23 14.
1
15.
3
16. Whatsimilaritiesand
differencearethere
betweentheequationsin
number14and15?
Sameslopes,differenty‐
intercepts
Topic:Solveequations
Solveeachequationfortheindicatedvariable.
17.3
2
5
8;Solveforx.
19.
5
2 ;Solveforx.
SDUHSDMath1Honors
18. 3
20.
6
22; Solveforn.
;Solvefory.
TE‐35 Name:
TransformationsandCongruence 6.2
Ready,Set,Go!
Ready
Topic:Basicrotationsandreflectionsofobjects
Ineachproblemtherewillbeapre‐imageandseveralimagesbasedonthegivenpre‐image.
Determinewhichoftheimagesarerotationsofthegivenpre‐imageandwhichofthemare
reflectionsofthepre‐image.Ifanimageappearstobecreatedastheresultofarotationanda
reflectionthenstateboth.
1.
Reflection
Pre‐Image
Rotation
Rotation
ImageA
ImageB
Rotation&
Reflection
ImageC
ImageD
2.
Rotation
Pre‐Image
ImageA
Rotation
ImageB
Rotation&
Reflection
ImageC
Rotation
ImageD
Topic:Defininggeometricshapesandcomponents
Foreachofthegeometricwordsbelowwriteadefinitionoftheobjectthataddressestheessential
elements.Also,listnecessaryattributesandcharacteristics.
3. Quadrilateral:Foursidedpolygon
4. Parallelogram:Quadrilateralwithtwopairsofparallelsides
5. Rectangle:Parallelogramwithfourrightangles
6. Square:Rectanglewithfourcongruentsides
7. Rhombus:Parallelogramwithfourcongruentsides
8. Trapezoid:Quadrilateralwithonepairofparallelsides
SDUHSDMath1Honors
TE‐36 Set
Topic:Reflectingandrotatingpoints
Foreachpairofpoint,PandP’,drawinthelineofreflectionthatwouldneedtobeusedtoreflectP
ontoP’.Thenfindtheequationofthelineofreflection.
10.
9.
Equation:
Equation:
Foreachpairofpoint,AandA’,drawinthelineofreflectionthatwouldneedtobeusedtoreflectA
ontoA’.Thenfindtheequationofthelineofreflection.Also,drawalineconnectingAtoA’andfind
theequationofthisline.ComparetheslopesofthelinesofreflectioncontainingAandA’.
12.
11.
EquationoftheLineofReflection:
EquationoftheLine ′:
SDUHSDMath1Honors
EquationoftheLineofReflection:
EquationoftheLine
′:
TE‐37 Topic:ReflectionsandRotations,composingreflectionstocreatearotation
13.
a. Whatistheequationforthelineofreflection
thatreflectspointPontoP’?
b. Whatistheequationforthelineofreflection
thatreflectspointP’ontoP’’?
c. CouldP’’alsobeconsideredarotationofpoint
P?Ifso,whatisthecenterofrotationandhow
manydegreeswaspointProtated?
Yes.Thecentercouldbeanypointonthe
perpendicularbisectorof ′
a. Whatistheequationforthelineofreflection
14.
thatreflectspointPontoP’?
. b. Whatistheequationforthelineofreflection
thatreflectspointP’ontoP’’?
c. CouldP’’alsobeconsideredarotationof
pointP?Ifso,whatisthecenterofrotation
andhowmanydegreeswaspointProtated?
Yes.Thecentercouldbeanypointonthe
perpendicularbisectorof ′
SDUHSDMath1Honors
TE‐38 Go
Topic:Slopesofparallelandperpendicularlinesandfindingbothdistanceandslopebetweentwopoints.
Writetheslopeofalineparalleltothegivenline.
15.
7
3
Writetheslopeofalineperpendiculartothegivenline.
4
16.
Findtheslopebetweenthegivenpairofpoints.Then,usingthePythagoreanTheorem,findthe
distancebetweenthepairofpoints.Youmayusethegraphtohelpyouasneeded.
17.
7, 5 2, 7 a. Slope:
b. Distance:
13
SDUHSDMath1Honors
TE‐39 Topic:Rotationsabouttheorigin
Plotthegivencoordinateandthenperformtheindicatedrotationaroundtheorigin,thepoint
andplottheimagecreated.Statethecoordinatesoftheimage.
18. Point 4, 2 rotate180°
CoordinatesforPoint , 20. Point
7, 3 rotate180°
CoordinatesforPoint , 19. Point
5, 3 rotate 90°
CoordinatesforPoint , 21. Point 1, 6 rotate 90°
CoordinatesforPoint , SDUHSDMath1Honors
,
,
TE‐52 Name:
TransformationsandCongruence 6.3H
Ready,Set,Go!
Ready
Topic:Polygons,definitionandnames
1. Whatisapolygon?Describeinyourownwordswhatapolygonis.
Answerswillvarybutshouldinclude:closedfigurewithstraightsidesandnocurves.
2. Fillinthenamesofeachpolygonbasedonthenumberofsidesthepolygonhas.
NumberofSides
NameofPolygon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
Topic:Rotationasatransformation
3. Whatfractionofaturndoesthewagonwheel
4. WhatfractionofaturndoesthemodelofaFerris
belowneedtoturninordertoappearthevery
wheelbelowneedtoturninordertoappearthe
sameasitdoesrightnow?Howmanydegreesof
verysameasitdoesrightnow?Howmany
rotationwouldthatbe?
degreesofrotationwouldthatbe?
ofaturn;
°
ofaturn;20°
SDUHSDMath1Honors
TE‐53 Set
Topic:Linesofsymmetryanddiagonals
5. Drawthelinesofsymmetryforeachregularpolygon,fillinthetableincludinganexpressionforthe
numberoflinesofsymmetryinan‐sidedpolygon.
Numberof
Numberoflines
Sides
ofsymmetry
3
3
4
4
5
5
6
6
7
7
8
8
n
n
6. Findallofthediagonalsineachregularpolygon.Fillinthetableincludinganexpressionforthenumber
ofdiagonalsinan‐sidedpolygon.
Numberof
Numberof
Sides
diagonals
3
0
4
2
5
5
6
9
7
14
8
20
n
7. Arealllinesofsymmetryalsodiagonals?Explain.
No,somelinesofsymmetrygothroughthemidpointsofoppositesidesoftheregularpolygons
whichmeansthattheselinesofsymmetryarenotdiagonalsofthepolygon.
SDUHSDMath1Honors
TE‐54 8. Arealldiagonalsalsolinesofsymmetry?Explain.
No,onlydiagonalsthatgothroughthecenterofregularpolygonsarelinesofsymmetry.
9. Whatshapeswillhavediagonalsthatarenotlinesofsymmetry?Namesomeanddrawthem.
Non‐regularpolygons
10. Willallparallelogramshavediagonalsthatarelinesofsymmetry?Ifso,drawandexplain.Ifnotdraw
andexplain.
Onlysquaresandrhombuseshavediagonalsthatarelinesofsymmetry.
Topic: Findinganglesofrotationforregularpolygons.
11. Findtheangle(s)ofrotationthatwillcarrythe12sidedpolygonbelowontoitself.
°
12. Whataretheanglesofrotation(lessthan360° fora20‐gon?Howmanylinesofsymmetry(linesof
reflection)willithave?
°, °, °, °, °,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°
20linesofsymmetry
13. Whataretheanglesofrotation(lessthan360° fora15‐gon?Howmanylineofsymmetry(linesof
reflection)willithave?
°, °, °, °,
°,
°,
°,
°,
°,
°,
°,
°,
°,
°
15linesofsymmetry
14. Howmanysidesdoesaregularpolygonhavethathasanangleofrotationequalto18°?Explain.
20sides
20linesofsymmetry
15. Howmanysidesdoesaregularpolygonhavethathasanangleofrotationequalto20°?Howmanylines
ofsymmetrywillithave?
18sides
18linesofsymmetry
SDUHSDMath1Honors
TE‐55 Go
Topic:Equationsforparallelandperpendicularlines.
Findtheequationofaline
PARALLELtothegiveninfo
andthroughtheindicated
point.
Findtheequationofaline
PERPENDICULARtothegiven
lineandthroughtheindicated
point.
16.Equationofaline:
4
1
a. Parallellinethroughpoint
1, 7 :
b. Perpendicularlinethough
point 1, 7 :
17.Tableofaline:
3
8
4
10
5
12
6
14
a. Parallellinethroughpoint
3, 8 :
b. Perpendiculartotheline
throughpoint 3, 8 :
18.Graphofaline:
a. Parallellinethroughpoint
2, 9 :
b. Perpendicularlinethrough
point 2, 9 :
SDUHSDMath1Honors
TE‐56 Topic:Reflectingandrotatingpointsonthecoordinateplane.
19.ReflectpointAoverthegivenlineofreflectionand 20. ReflectparallelogramABCDoverthegiven
labeltheimageA’.
lineofreflectionandlabeltheimageA’B’C’D’.
22. GivenparallelogramQRSTanditsimage
Q’R’S’T’drawthelineofreflectionthatwas
used.
21. ReflecttriangleABCoverthegivenlineof
reflectionandlabeltheimageA’B’C’.
23. UsingpointPasacenterofrotation.Rotatepoint
Q 120°aboutpointPandlabeltheimageQ’.
24. UsingpointCasthecenterorrotation.Rotate
pointR270°aboutpointCandlabeltheimage
R’.
SDUHSDMath1Honors
TE‐64 Name:
TransformationsandCongruence 6.4H
Ready,Set,Go!
Ready
Topic:Definingcongruenceandsimilarity.
1. Whatdoyouknowabouttwofiguresiftheyarecongruent?
Samesidelengthsandsameanglemeasurements
2. Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresarecongruent?
Thereisasequenceofrigidmotionsthatmaponeontotheother.
3. Whatdoyouknowabouttwofiguresiftheyaresimilar?
Sameshape(anglemeasuresarethesame)butdifferentsidelengths.
4. Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresaresimilar?
Thereisadilationthatmapsoneontotheother.
Set
Topic:Classifyingquadrilateralsbasedontheirproperties.
Usingtheinformationgivendeterminethemostspecificclassificationofthequadrilateral.
5. Has180°rotationalsymmetry.
6. Has90°rotationalsymmetry.
Parallelogram
Square
7. Hastwolinesofsymmetrythatarediagonals.
8. Hastwolinesofsymmetrythatarenot
diagonals.
Rhombus
Rectangle
9. Hascongruentdiagonals.
10. Hasdiagonalsthatbisecteachother.
Rectangle
Parallelogram
11. Hasdiagonalsthatareperpendicular.
12. Hascongruentangles.
Rhombus
Rectangle
SDUHSDMath1Honors
TE‐65 Go
Topic:Slopeanddistance
Findtheslopebetweeneachpairofpoints.Then,usingthePythagoreanTheorem,findthedistance
betweeneachpairofpoints.
14. 7, 1 11, 7
13.
3, 2 0, 0 a. Slope
b. Distance:
a. Slope
b. Distance:
2
√ √ 15.
10, 13 a. Slope
5, 1 b. Distance:
13
17. 5, 22 17, 28 a. Slope
b. Distance:
√ SDUHSDMath1Honors
16.
6, 3 3, 1
a. Slope
18. 1, 7 6, 5
a. Slope
b. Distance:
√
b. Distance:
13
TE‐66 Topic:Similarandcongruentfigures
Determinewhichletterbestdescribestheshapesshown.
19.
20.
21.
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
22.
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
24.
23.
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
26.
25.
a.
b.
c.
d.
Theshapesareonlycongruent
Theshapesareonlysimilar
Theshapesarebothsimilarandcongruent
Theshapesareneithersimilarnorcongruent
SDUHSDMath1Honors
TE‐74 Name:
TransformationsandCongruence 6.5H
Ready,Set,Go!
Ready
Topic:Performingasequenceoftransformations
Thegivenfiguresaretobeusedaspre‐images.Performthestatedtransformationstoobtainan
image.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 .Labeltheimage
A’’B’’C’’D’’.
SDUHSDMath1Honors
TE‐75 Topic:Findthesequenceoftransformations.
Findthesequenceoftransformationsthatwillcarry∆
onto∆ ’ ’ ’.Clearlydescribethesequenceof
transformationsbeloweachgrid.
3.
4.
Translate8unitsup,rotate
°
aboutpointT,andreflectabout
Translate8unitsleft,reflectover
.
.
Set
Topic:Trianglecongruencies
Explainwhetherornotthetrianglesarecongruent,similar,orneitherbasedonthemarkingsthat
indicatecongruence.
5.
6.
Congruent
Similar
8.
7.
Neither
SDUHSDMath1Honors
Congruent
TE‐76 9.
10.
Neither
Congruent
Usethegivencongruencestatementtodrawandlabeltwotrianglesthathavetheproper
correspondingpartscongruenttooneanother.
11.∆ABC ≅ ∆PQR
12. ∆
≅∆
Go
Topic:Graphingfunctionsandmakingcomparisons.
Grapheachpairoffunctionsandmakeanobservationabouthowthefunctionscomparetooneanother.
14.
2
2
13.
2 2
Thelineshavethesamey‐intercept
SDUHSDMath1Honors
Thecurvesarereflectionsoverthex‐axis.
TE‐77 Topic:Reviewoffindingrecursiverulesforsequences
Usethegivensequenceofnumberstowritearecursiveruleforthenthvalueofthesequence.
15.3, 6, 12, 24, …
, 1, …
16. , 0,
,
⋅
,
Topic:Trianglecongruenceproperties
Questions#17‐20canbecompletedbygoingto:http://illuminations.nctm.org/Activity.aspx?id=3504
Investigatecongruencebymanipulatingtheparts(sidesandangles)ofatriangle.Ifyoucancreate
twodifferenttriangleswiththesameparts,thenthosepartsdonotprovecongruence.Canyouprove
allthetheorems(SAS,,SSA,SSS,AAS,ASA,AAA)?
17. Eachtrianglecongruencetheoremusesthreeelements(sidesandangles)toprovecongruence.Select
threetriangleelementsfromthetop,rightmenutostart.(Note:Thetooldoesnotallowyoutoselect
morethanthreeelements.Ifyouselectthewrongelement,simplyunselectitbeforechoosinganother
element.)Thiscreatesthoseelementsintheworkarea.
Onthetopofthetoolbar,thethreeelementsarelistedinorder.Forexample,ifyouchoosesideAB,angle
A,andangleB,youwillbeworkingonAngle–Side–Angle.IfinsteadyouchoosesideAB,angleA,and
angleC,youwillbeworkingonAngle–Angle–Side.Thetwotheoremsaredifferent,eventhoughboth
involvetwoanglesandoneside.
18. Constructyourtriangle:
 Movetheelementsofthetrianglesothatpointslabeledwiththesamelettertouch.
 Clickanddragadottomovetheelementtoanewlocation.
 Clickanddragaside'sendpointorangle'sarrowtorotatetheelement.Thecenterofrotationisthe
side'smidpointortheangle'svertex,respectively.
 Tohelpplaceelements,pointsmarkedwiththesamelettersnaptogether.Whenanglessnap,the
raysareextendedtotheedgeoftheworkarea.
 Whenyoucreateaclosedtriangle,thepointsmergeandcenterisfilledin.
 Onceatriangleisformedwiththeoriginalthreeelements,thetrianglemovestothebottom,right
corneroftheworkarea,andcongruentelementsappear.
SDUHSDMath1Honors
TE‐87 Name:
TransformationsandCongruence 6.6H
Ready,Set,Go!
Ready
Topic:Correspondingpartsoffiguresandtransformations
Giventhefiguresineachsketchwithcongruentanglesandsidesmarked,firstlistthepartsofthe
figuresthatcorrespond(Forexample,in#3,∠ ≅ ∠ ).Thendetermineifareflectionoccurredas
partofthesequenceoftransformationsthatwasusedtocreatetheimage.
1.
Congruencies
∠ ≅∠ ≅
≅
Reflected?YesorNo
2.
SDUHSDMath1Honors
Congruencies
≅
≅
∠ ≅∠ ∠ ≅∠ ∠ ≅∠ ∠ ≅∠ Reflected?YesorNo
TE‐88 Set
Topic:Usecongruenttrianglecriteriaandtransformationstojustifyconjectures.
Ineachproblembelowtherearesometruestatementslisted.Fromthesestatementsaconjecture(a
guess)aboutwhatmightbetruehasbeenmade.Usingthegivenstatementsandconjecture
statementcreateanargumentthatjustifiestheconjecture.
Conjecture: ∠ ≅ ∠
3. Truestatements:
a. Istheconjecturecorrect?Yes
PointMisthemidpointof ∠
≅∠
b. Argumenttoproveyouareright:
≅
ThetwotrianglesarecongruentbySAS.Therefore,the
correspondingpartsarecongruent.
4. Truestatements:
∠
≅∠
≅
bisects∠
Conjecture:
a. Istheconjecturecorrect?Yes
b. Argumenttoproveyouareright:
ThetwotrianglesarecongruentbySAS.Therefore,
correspondingpartsarecongruentsince∠
≅∠
bisects∠
SDUHSDMath1Honors
5. Truestatements:
isa180°rotationof
∆
∆
and
≅∆
Conjecture: ∆
a. Istheconjecturecorrect?Yes
b. Argumenttoproveyouareright:
Arotationmaps∆
only
.Therefore,∆
≅∆
,
≅
,
≅
.∠
≅∠
because∠
≅
∠
andtheyare2linearpairs∠
&∠
and
∠
&∠
.Therefore,thetrianglesarecongruentbySAS.
TE‐89 Go
Topic:Createbothexplicitandrecursiverulesforthevisualpatterns.
6. Findanexplicitfunctionruleandarecursiverulefordotsinstepn.
Step1
Step2
Step3
Explicit:
Recursive:
,
7. Findanexplicitfunctionruleandarecursiveruleforsquaresinstepn.
Explicit:
Recursive:
,
Findanexplicitfunctionruleandarecursiveruleforthevaluesineachtable.
10.
9.
8.
Step
Value
1
1
2
16
1
5
2
11
3
8
2
25
3
21
4
4
3
125
4
31
5
2
4
625
Explicit:
Explicit:
Explicit:
Recursive:
,
Recursive:
Recursive:
⋅ Topic:Reviewofsolvingequations.
Solveeachequationfort.
12. 10
4
12 3 11.
13
SDUHSDMath1Honors
⋅
TE‐98 Name:
Constructions 6.7H
Ready,Set,Go!
Ready
Topic:Transformationsoflines
Foreachsetoflinesusethepointsonthelinetodeterminewhichlineistheimageandwhichisthe
pre‐image,labelthem,writeimagebytheimagelineandpreimagebytheoriginalline.Thendefine
thetransformationthatwasusedtocreatetheimage.Finallyfindtheequationforeachline.
2.
1.
a. DescriptionofTransformation:
translated4unitsup
b. Equationforpre‐image:
c. Equationforimage:
SDUHSDMath1Honors
a. DescriptionofTransformation:
Reflectabout
b. Equationforpre‐image:
c. Equationforimage:
TE‐99 Set
Topic: Trianglecongruenceproperties
3. Truestatements:
Conjecture:
≅
∠
≅∠
a. Istheconjecturecorrect?Yes
∠ ≅∠ b. Argumenttoproveyouareright:
≅
≅
because
ThetrianglesarecongruentASA.Therefore,
theyarecorrespondingpartsofcongruenttriangles.
4. Truestatements:
∠
≅∠
≅
bisects∠
Conjecture:
a. Istheconjecturecorrect?Yes
b. Argumenttoproveyouareright:
ThetrianglesarecongruentbySAS.Therefore,∠
≅∠
becausetheyarecorrespondingpartsofcongruenttriangles.
5. Truestatements:
Wisthemidpointof
≅ isperpendicularto Conjecture:
a. Istheconjecturecorrect?Yes
b. Argumenttoproveyouareright:
ThetrianglesarecongruentbySSS.Therefore,∠
≅∠
becausetheyarecorrespondingpartsofcongruenttriangles.
Theyare
°togetherand °each.
SDUHSDMath1Honors
TE‐100 Topic:Geometricconstructions
6. Accordingtotheconstructionshowninthediagramtotheright,
whatdowecallsegment ?
Altitudeof∆
fromBto 7. Whatdotheconstructionmarksinthefigurebelowcreate?
Perpendicularbisectorof
8. Whichdiagramshowstheconstructionofanequilateraltriangle?
a.
b.
c.
d.
Go
Topic:Solvingsystemsofequations
Solveeachsystemofequations.Utilizesubstitutionorelimination.
11
4
9
9
9.
10.
2
19
3
6
,
, SDUHSDMath1Honors
2
4
11.
,
11
2
TE‐101 12.
2
,
1
1
13.
SDUHSDMath1Honors
2
3
,
7
8
14.
4
6
2
7
,
8
TE‐109 Name:
Constructions 6.8H
Ready,Set,Go!
Ready
Topic:Transformationsoflines,algebraicandgeometricthoughts.
Foreachsetoflinesusethepointsonthelinetodeterminewhichlineistheimageandwhichisthe
pre‐image,labelthem,writeimagebytheimagelineandpreimagebytheoriginalline.Thendefine
thetransformationthatwasusedtocreatetheimage.Finallyfindtheequationforeachline.
2.
1.
a. DescriptionofTransformation:
a. DescriptionofTransformation:
Translateleft7
b. Equationforpre‐image:
Rotate
°aboutP
b. Equationforpre‐image:
c. Equationforimage:
c. Equationforimage:
SDUHSDMath1Honors
TE‐110 Set
Topic:Transformationsandtrianglecongruence.
Determinewhetherornotthestatementistrueorfalse.Iftrue,explainwhy.Iffalse,explainwhynot
orprovideacounterexample.
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:Geometricconstructions
8. Whenfinishedwiththeconstructionfor“CopyanAngle”,segmentsaredrawnconnectingwherethearcs
crossthesidesoftheangles.Whatmethodprovesthesetwotrianglestobecongruent?
a. ASA b.SAS c.SSS d.AAS
SDUHSDMath1Honors
TE‐111 9. Whichillustrationshowsthecorrectconstructionofananglebisector?
a.
b.
Go
c.
d.
Topic:Trianglecongruenceandpropertiesofpolygons.
10. Whatistheminimumamountofinformationneededtodeterminethattwotrianglesarecongruent?List
allpossiblecombinationsofneededcriteria.
3piecesofinformation(anglesand/orsides)areneededtodeterminethattwotrianglesare
congruent.
Possiblecombinationsofneededcriteria:SSS,ASA,SAS,AAS
11. Whatisalineofsymmetryandwhatisadiagonal?Aretheythesamething?Couldtheybethesameina
polygon?Ifsogiveanexample,ifnotexplainwhynot.
Alineofsymmetrycutsthediagonalintotwocongruentshapesthataremirrorimagesofeach
other.
Adiagonalconnectstwonon‐adjacentvertices
12. Howisthenumberoflinesofsymmetryforaregularpolygonconnectedtothenumberofsidesofthe
polygon?Howisthenumberofdiagonalsforapolygonconnectedtothenumberofsides?
Thenumberoflinesofsymmetryforaregularpolygonisthesameasthenumberofsidesofthe
polygon.
wherenisthenumberofsides.
Thenumberofdiagonalsisequationto
13. Whatdorighttriangleshavetodowithfindingdistancebetweenpointsonacoordinategrid?
ThePythagoreanTheoremcanbeusedtofindthedistancebetweenpointsonthecoordinate
grid.
SDUHSDMath1Honors
TE‐112 Topic:Findingdistanceandslope.
Foreachpairofgivencoordinatepointsfinddistancebetweenthemandfindtheslopeoftheline
thatpassesthroughthem.Showallyourwork.
15. 16, 45
34, 75
14. 10, 31 20, 11 a. Slope:
b. Distance:
a. Slope:
b. Distance:
130
√ 16. 8, 21 20, 11 a. Slope:
b. Distance:
√ SDUHSDMath1Honors
17.
10, 0
14, 18
a. Slope:
b. Distance:
30
TE‐127 Module6ReviewHomework
1. Describethesequenceofrigidmotionsthatshows∆
≅∆
Reflectoverthex‐axisandthentranslateright4units.
.
2. Usethecoordinategrid,below,tocompleteparts(a)–(c).
a. Reflect∆
acrosstheverticalline,paralleltothe ‐axis,goingthroughpoint 1, 0 .Labelthe
transformedpoints
as , , ,respectively.
SeeimageinREDbelow.
acrossthehorizontalline,paralleltothe ‐axisgoingthroughpoint 0, 1 .Label
b. Reflect∆
,respectively.
thetransformedpointsof ’ ’ ’as
SeeimageinBLUEbelow.
.
c. Describeasinglerigidmotionthatwouldmap∆
to∆
Rotation
°abouttheorigin.
SDUHSDMath1Honors
TE‐128 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.Labelthe
imageas ′′′ ′′′ ′′′.
SeeimageinGREEN.
SDUHSDMath1Honors
TE‐129 5. Pre‐image: 3, 1 ,
2, 1 ,
2, 2 Performthefollowingsequenceoftransformations:
Reflecttheimageoverthegivenline(lineL),then
rotate180°aroundtheorigin,thentranslateup5
units.
Topic:Rotationsymmetryforregularpolygonsandtransformations
6. Whatanglesofrotationalsymmetryarethereforaregularpentagon?
72°,144°,216°,288°,360°
7. Whatanglesofrotationalsymmetryarethereforaregularhexagon?
60°,120°,180°,240°,300°,360°
8. Ifaregularpolygonhasanangleofrotationalsymmetrythatis40°,howmanysidesdoesthepolygon
have?
9sides
SDUHSDMath1Honors
TE‐130 Oneachgivencoordinategridbelowperformtheindicatedtransformation.
10. RotateP 90° aroundpointC.
9. ReflectpointPoverlinej.
Topic:Connectingtableswithtransformations.
Foreachfunctionfindtheoutputsthatfillinthetable.Thendescribethe
relationshipbetweentheoutputsineachtable.
2 12.
4
2
3
11.
1
2
1
1
4
2
4
2
2
16
3
6
3
0
3
64
4
8
4
2
4
256
SDUHSDMath1Honors
4
1
2
3
1
4
4
Relationshipbetween
and
isalways6lessthan
:
Relationshipbetweent(x)andh(x):
isalways3stepsbehind
TE‐131 Ineachfigurefindandmarkatleastfourpossiblecentersofrotationthatwouldworkforrotating
thepre‐imagepointtotheimagepoint.
13.
14.
Centersofrotation: Answersmayvary.
.
Anypointontheline
Centersofrotation: Answersmayvary.
Anypointonthelines
.
Findthepointofrotationthatmapseachpre‐imagetotheimage.
15.
16.
,
SDUHSDMath1Honors
,
TE‐132 Findthelineofreflectionthatmapseachpre‐imagetotheimage.
17.
18.
Topic:Constructingregularpolygonsinscribedinacircle
19. Constructanisoscelestrianglethatincorporates asoneofthesides.Constructthecirclethat
circumscribesthetriangle.
SDUHSDMath1Honors
TE‐133 20. Constructahexagonthatincorporates
hexagon.
21. Constructasquarethatincorporates
square.
SDUHSDMath1Honors
asoneofthesides.Constructthecirclethatcircumscribesthe
asoneofthesides.Constructthecirclethatcircumscribesthat
IntrotoModule7Honors‐GotheDistance
ADevelopUnderstandingTask
TheperformancesofthePodunkHighSchooldrillteamareverypopularduringhalf‐
timeattheschool’sfootballandbasketballgames.WhenthePodunkHighSchool
drillteamchoreographsthedancemovesthattheywilldoonthefootballfield,they
layouttheirpositionsonagridliketheonebelow:
Inoneoftheirdances,theyplantomakepatternsholdinglong,wideribbonsthatwillspanfromonedancer
inthemiddletosixotherdancers.Onthegrid,theirpatternlookslikethis:
Thequestionthedancershaveishowlongtomaketheribbons.Somedancersthinkthattheribbonfrom
Gene(G)toCasey(C)willbeshorterthantheonefromGene(G)toBailey(B).
1. Howlongdoeseachribbonneedtobe?
EachRibbonneedstobe5unitslong
2. Explainhowyoufoundthelengthofeachribbon.
UsePythagoreanTheoremforeachribbon,exceptforGFandGC.
SDUHSDMath1Honors
TE‐134 TE‐135 Whentheyhavefinishedwiththeribbonsinthisposition,theyareconsideringusingthemtoformanew
patternlikethis:
3. WilltheribbonstheyusedinthepreviouspatternbelongenoughtogobetweenBailey(B)andCasey(C)
inthenewpattern?Explainyouranswer.
Yes,becausetheywillonlyneed√ √ units,whichislessthan5.
SDUHSDMath1Honors
TE‐136 Genenoticesthatthecalculationssheismakingforthelengthoftheribbonsremindsherofmathclass.She
saystothegroup,“Hey,Iwonderifthereisaprocessthatwecoulduselikewhatwehavebeendoingtofind
thedistancebetweenanytwopointsonthegrid.”Shedecidestothinkaboutitlikethis:
“I’mgoingtostartwithtwopointsanddrawthelinebetweenthemthatrepresentsthedistancethatI’m
andB ,
.Hmmmm....
lookingfor.Sincethesetwopointscouldbeanywhere,InamedthemA ,
whenIfiguredthelengthoftheribbons,whatdidIdonext?”
4. Thinkbackontheprocessyouusedtofindthelengthoftheribbonandwritedownyourstepshere,
usingpointsAandB.
5. Usetheprocessyoucameupwithinquestion4tofindthedistancebetweentwopointslocatedat
1, 5 and 2, 6 √
6. Useyourprocesstofindtheperimeterofthehexagonpatternshownabovequestion3.
√ SDUHSDMath1Honors
IntrotoModule7Honors‐Ready,Set,Go!
Ready
Topic:Findingthedistancebetweentwopoints
Usethenumberlinetofindthedistancebetweenthegivenpoints.(Note:The
notationABmeansthedistancebetweenpointsAandB.)
1. AE
2. GB
3. BF
6
7.5
6
4. Describeawaytofindthedistancebetweentwopointsonanumberlinewithoutcountingthespaces. Findtheabsolutevalueofthedifferencebetweenthepoints
Topic:Graphinglines.
Thegraphattherightisoftheline
.
5. Onthesamegrid,graphaparallellinethatis4unitsbelowit.
Dashedlineatright
6. Writetheequationofthenewline.
7. Writethey‐interceptofthenewlineasanorderedpair.
,
8. Writethex‐interceptasanorderedpair.
, 9. a. Writetheequationofthenewlineinpoint‐slopeform
usingthey‐intercept
b. Writetheequationofthenewlineinpoint‐slopeformusingthex‐intercept.
c. Explaininwhatwaytheequationsin5aand5barethesameandinwhatwaytheyaredifferent.
Simplifiedequationsareequivalent.Differenceisinthestartingpoint.
SDUHSDMath1Honors
TE‐137 TE‐138 Set
Topic:Slopetrianglesandthedistanceformula.
∆
isaslopetrianglefor whereBCistheriseandACistherun.Noticethatthelengthof hasa
correspondinglengthonthey‐axisandthelengthof hasacorrespondinglengthonthex‐axis.Theslope
formulaiswrittenas
wheremistheslope.
10. a. Whatdoesthevalue
tellyou?
theverticaldistance
tellyou?
b. Whatdoesthevalue
thehorizontaldistance
Inthepreviousmoduleyoufoundthelengthofaslantedlinesegmentbydrawingtheslopetriangleand
performingthePythagoreanTheorem.Inthisexercisetrytodevelopamoreefficientmethodoffindingthe
and
combinedwiththePythagorean
lengthofalinesegmentbyusingthemeaningof
Theorem.
12. FindAB
11. FindAB
√
.
SDUHSDMath1Honors
TE‐139 Go
Topic:Rectangularcoordinates
Usethegiveninformationtofillinthemissingcoordinates.Thenfindthelengthoftheindicatedline
segment.
Coordinatesongraphsareintentionallyleftblank
13. a. FindHB
20
b. FindBD
10
Topic:Writingequationsoflines.
Writetheequationofthelineinpoint‐slopeformusingthegiveninformation.
15. 11, 3 , 6, 2
14. Slope= point(12,5)
16. x‐intercept: 2,y‐intercept:‐3
18. Slope:
,x‐intercept:5
SDUHSDMath1Honors
19.
10,17 ,
17. Allx valuesare‐7,y canbeanything
13, 17 TE‐140 EndofModule6HonorsChallengeProblems
ThefollowingproblemsareintendedforstudentstoworkonafterModule6HTest.Theproblemsfocuson
usingsimilartrianglestofindarea.ThenextmodulebuildsontheideaofconnectingAlgebraandGeometry.
Thefollowingpageisblankfortheteachertocopyandgivetoeachstudentafterthetest.Belowarethe
solutions.
BothrighttriangleABCandisoscelestriangleBCD,shownhere,haveheight5cmfrombase
12cm.Use
thefigureandinformationprovidedtoanswerthefollowingquestions.
1. WhatistheabsolutedifferencebetweentheareasofΔABCandΔBCD?
TheareasofΔABCandΔBCDcanbedenotedby[ΔABC]and[ΔBCD],respectively.Thisnotation
willbeusedtodenotetheareasofthetrianglesthroughoutthissolutionset.SinceΔABCand
.Therefore,
ΔBCDbothhavebase
cmandheight5cm,itfollowsthat
becausethetwotriangleshavethesamearea,theabsolutedifferenceintheareasis
.
2. WhatistheratiooftheareaofΔABEtoΔCDE?
Fromthefigure,weseethat
.Similarly,
.
Again,since
,wecanwritethefollowingequation:
,sotheratio
.
.Whensimplified,wehave
3. WhatistheareaofΔBCE?
ThefigureshowsaltitudeEYofΔBCEandaltitudeDXofΔBCD,bothdrawnperpendiculartobase
BC.Noticethat
~
,whichmeansthelengthsofcorrespondingsidesareproportionate.
cm2.
Also,noticethat
~
.Itfollows,then,that
4. WhatistheareaofpentagonABCDE?
Therefore,theareaofpentagonABCDEis
–
–
–
2
cm .
SDUHSDMath1Honors