SECONDARY MATH II // MODULE 6
SIMILARITY & RIGHT TRIANGLE TRIGONOMETRY – 6.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
6. 2 Triangle Dilations
A Solidify Understanding Task
1. GivenΔABC,usepointMasthecenterofadilationtolocatetheverticesofatrianglethathassidelengthsthatarethreetimeslongerthanthesidesofΔABC.
2. NowusepointNasthecenterofadilationtolocatetheverticesofatrianglethathassidelengthsthatareone-halfthelengthofthesidesofΔABC.
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SECONDARY MATH II // MODULE 6
SIMILARITY & RIGHT TRIANGLE TRIGONOMETRY – 6.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
3. Labeltheverticesinthetwotrianglesyoucreatedinthediagramabove.Basedonthisdiagram,writeseveralproportionalitystatementsyoubelievearetrue.Firstwriteyourproportionalitystatementsusingthenamesofthesidesofthetrianglesinyourratios.Thenverifythattheproportionsaretruebyreplacingthesidenameswiththeirmeasurements,measuredtothenearestmillimeter.
Mylistofproportions:(trytofindatleast10proportionalitystatementsyoubelievearetrue)
4. Basedonyourworkabove,underwhatconditionsarethecorrespondinglinesegmentsinanimageanditspre-imageparallelafteradilation?Thatis,whichwordbestcompletesthisstatement?
Afteradilation,correspondinglinesegmentsinanimageanditspre-imageare[never,
sometimes,always]parallel.
5. Givereasonsforyouranswer.Ifyouchoose“sometimes”,beveryclearinyourexplanationabouthowyoucantotellwhenthecorrespondinglinesegmentsbeforeandafterthedilationareparallelandwhentheyarenot.
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SECONDARY MATH II // MODULE 6
SIMILARITY & RIGHT TRIANGLE TRIGONOMETRY – 6.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
GivenΔABC,usepointAasthecenterofadilationtolocatetheverticesofatrianglethathassidelengthsthataretwiceaslongasthesidesofΔABC.
6. Explainhowthediagramyoucreatedabovecanbeusedtoprovethefollowingtheorem:
Thesegmentjoiningmidpointsoftwosidesofatriangleisparalleltothethirdsideandhalfthe
length.
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Dilations preserve a measure
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ABC LABC andACBLACB
This is parrallel a half length
