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.

CC

BY

Ham

mad

Kah

n

http

s://f

lic.k

r/p/

sczw

A1

Page 7

MHAFox'T Fom gMto C1.75 3

5.25

of Tao

BOB

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.

Page 8

y MA MI

FI AFT MT mi

0

Alwaysexceptwhencenterofdilation

is on agivenpointof thepreimage

tobedilated

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.

Page 9

A to B 742 AtoC It 24t p toilf Han B 3

pg

Dilations preserve a measure

B is midpoint ofART Cis midpoint

AI Since Dilations presereLmeasure

ABC LABC andACBLACB

This is parrallel a half length