6.7 quadrilaterals—beyond definition e n · secondary math i // module 6 transformations and...
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
6.7 Quadrilaterals—Beyond
Definition
A Practice Understanding Task
Wehavefoundthatmanydifferentquadrilateralspossesslinesofsymmetryand/orrotational
symmetry.Inthefollowingchart,writethenamesofthequadrilateralsthatarebeingdescribedin
termsoftheirsymmetries.
Whatdoyounoticeabouttherelationshipsbetweenquadrilateralsbasedontheirsymmetriesand
highlightedinthestructureoftheabovechart?
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Basedonthesymmetrieswehaveobservedinvarioustypesofquadrilaterals,wecanmakeclaims
aboutotherfeaturesandpropertiesthatthequadrilateralsmaypossess.
1.Arectangleisaquadrilateralthatcontainsfourrightangles.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutrectanglesbesidesthe
definingpropertythat“allfouranglesarerightangles?”Makealistofadditionalpropertiesof
rectanglesthatseemtobetruebasedonthetransformation(s)oftherectangleontoitself.Youwill
wanttoconsiderpropertiesofthesides,theangles,andthediagonals.Thenjustifywhythe
propertieswouldbetrueusingthetransformationalsymmetry.
2.Aparallelogramisaquadrilateralinwhichoppositesidesareparallel.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutparallelogramsbesides
thedefiningpropertythat“oppositesidesofaparallelogramareparallel?”Makealistofadditional
propertiesofparallelogramsthatseemtobetruebasedonthetransformation(s)ofthe
parallelogramontoitself.Youwillwanttoconsiderpropertiesofthesides,anglesandthediagonals.
Thenjustifywhythepropertieswouldbetrueusingthetransformationalsymmetry.
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.Arhombusisaquadrilateralinwhichallfoursidesarecongruent.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutarhombusbesidesthe
definingpropertythat“allsidesarecongruent?”Makealistofadditionalpropertiesofrhombuses
thatseemtobetruebasedonthetransformation(s)oftherhombusontoitself.Youwillwantto
considerpropertiesofthesides,anglesandthediagonals.Thenjustifywhythepropertieswouldbe
trueusingthetransformationalsymmetry.
4.Asquareisbotharectangleandarhombus.
Basedonwhatyouknowabouttransformations,whatcanwesayaboutasquare?Makealistof
propertiesofsquaresthatseemtobetruebasedonthetransformation(s)ofthesquaresontoitself.
Youwillwanttoconsiderpropertiesofthesides,anglesandthediagonals.Thenjustifywhythe
propertieswouldbetrueusingthetransformationalsymmetry.
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Inthefollowingchart,writethenamesofthequadrilateralsthatarebeingdescribedintermsof
theirfeaturesandproperties,andthenrecordanyadditionalfeaturesorpropertiesofthattypeof
quadrilateralyoumayhaveobserved.Bepreparedtosharereasonsforyourobservations.
Whatdoyounoticeabouttherelationshipsbetweenquadrilateralsbasedontheircharacteristics
andthestructureoftheabovechart?
Howarethechartsatthebeginningandendofthistaskrelated?Whatdotheysuggest?
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
6.7
READY Topic:Definingcongruenceandsimilarity.
1.Whatdoyouknowabouttwofiguresiftheyarecongruent?2.Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresarecongruent?3.Whatdoyouknowabouttwofiguresiftheyaresimilar?4.Whatdoyouneedtoknowabouttwofigurestobeconvincedthatthetwofiguresaresimilar? SET Topic:Classifyingquadrilateralsbasedontheirproperties.Usingtheinformationgivendeterminethemostaccurateclassificationofthequadrilateral.5.Has1800rotationalsymmetry. 6.Has900rotationalsymmetry.7.Hastwolinesofsymmetrythatarediagonals. 8.Hastwolinesofsymmetrythatarenot diagonals.9.Hascongruentdiagonals. 10.Hasdiagonalsthatbisecteachother.11.Hasdiagonalsthatareperpendicular. 12.Hascongruentangles.
READY, SET, GO! Name PeriodDate
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY – 6.7
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
6.7
GO Topic:Slopeanddistance.Findtheslopebetweeneachpairofpoints.Then,usingthePythagoreanTheorem,findthedistancebetweeneachpairofpoints.Distancesshouldbeprovidedinthemostexactform.13.(-3,-2),(0,0) a.Slope:b.Distance:
14.(7,-1),(11,7) a.Slope:b.Distance:
15.(-10,13),(-5,1)a.Slope:b.Distance:
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:
S
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