SECONDARY MATH I // MODULE 6 TRANSFORMATIONS AND SYMMETRY 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 line 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?
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SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
6. 7 Quadrilaterals—Beyond Definition
A Practice Understanding Task
Wehavefoundthatmanydifferentquadrilateralspossesslineand/orrotationalsymmetry.
Inthefollowingchart,writethenamesofthequadrilateralsthatarebeingdescribedintermsof
theirsymmetries.
Whatdoyounoticeabouttherelationshipsbetweenquadrilateralsbasedontheirsymmetriesand
highlightedinthestructureoftheabovechart?
SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Basedonthesymmetrieswehaveobservedinvarioustypesofquadrilaterals,wecanmakeclaims
aboutotherfeaturesandpropertiesthatthequadrilateralsmaypossess.
1.Arectangleisaquadrilateralthatcontainsfourrightangles.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutrectanglesbesidesthe
definingpropertythatallfouranglesarerightangles?Makealistofadditionalpropertiesof
rectanglesthatseemtobetruebasedonthetransformation(s)oftherectangleontoitself.Youwill
wanttoconsiderpropertiesofthesides,theangles,andthediagonals.
2.Aparallelogramisaquadrilateralinwhichoppositesidesareparallel.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutparallelograms
besidesthedefiningpropertythatoppositesidesofaparallelogramareparallel?Makealistof
additionalpropertiesofparallelogramsthatseemtobetruebasedonthetransformation(s)ofthe
parallelogramontoitself.Youwillwanttoconsiderpropertiesofthesides,anglesandthe
diagonals.
SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.Arhombusisaquadrilateralinwhichallfoursidesarecongruent.
Basedonwhatyouknowabouttransformations,whatelsecanwesayaboutarhombusbesidesthe
definingpropertythatallsidesarecongruent?Makealistofadditionalpropertiesofrhombuses
thatseemtobetruebasedonthetransformation(s)oftherhombusontoitself.Youwillwantto
considerpropertiesofthesides,anglesandthediagonals.
4.Asquareisbotharectangleandarhombus.
Basedonwhatyouknowabouttransformations,whatcanwesayaboutasquare?Makealistof
propertiesofsquaresthatseemtobetruebasedonthetransformation(s)ofthesquaresontoitself.
Youwillwanttoconsiderpropertiesofthesides,anglesandthediagonals.
SECONDARY MATH I // MODULE 6
TRANSFORMATIONS AND SYMMETRY
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
Inthefollowingchart,writethenamesofthequadrilateralsthatarebeingdescribedintermsof
theirfeaturesandproperties,andthenrecordanyadditionalfeaturesorpropertiesofthattypeof
quadrilateralyoumayhaveobserved.Bepreparedtosharereasonsforyourobservations.
Whatdoyounoticeabouttherelationshipsbetweenquadrilateralsbasedontheircharacteristics
andhighlightedinthestructureoftheabovechart?
Howarethechartsatthebeginningandendofthistaskrelated?Whatdotheysuggest?
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