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 We have found that many different quadrilaterals possess lines of symmetry and/or rotational symmetry. In the following chart, write the names of the quadrilaterals that are being described in terms of their symmetries. What do you notice about the relationships between quadrilaterals based on their symmetries and highlighted in the structure of the above chart? CC BY Gabrielle https://flic.kr/p/9tKTTn 36
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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?
CC
BY
Gab
riel
le
http
s://f
lic.k
r/p/
9tK
TT
n
36
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.
38
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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