SECONDARY MATH II // MODULE 5

GEOMETRIC FIGURES – 5.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

5. Given:!" ∥ !"Prove:Same-sideinteriorangles∠3and∠5aresupplementary

.6. Given:Alternateinteriorangles∠3and∠6arecongruentProve:!" ∥ !"

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40 43S R

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1 Sincealternate interiorangles13and26 All congruent we canrotate

aroundpointM themidpoint of APTuntilhecoincides

with L32 SinceAM

andB Al collinearforAtocoincidewithBtheangleof

rotationmusthavebeen180

gAftertherotationAC andDwill lieonEffBasedon the

parallelpostulaterotating

Tf twoaboutMproducesanimagelinethatis

parallel toEBandwehaveshownthatthisline

coincideswithEFTherboreEFIlip

SECONDARY MATH II // MODULE 5

GEOMETRIC FIGURES – 5.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.6

Needhelp?Visitwww.rsgsupport.org

READY

Topic:Recallingfeaturesoftherigid-motiontransformations

Completeeachstatement

1. WhenIuselinesegmentstoconnectthecorrespondingpointsofapre-imageandtheimageinatranslation,thelinesegmentsare________________________________and____________________________________because_______________________________________________________________________________________________________

2. WhenIuselinesegmentstoconnectthecorrespondingpointsofapre-imageandtheimageinareflection,thelineofreflectionisthe__________________________________________ofthesegmentsbecause_________________________________________________________________________________________________________________

3. Inarotation,thecorrespondingpointsofthepre-imageandtheimagearethesame__________________________fromthecenterofrotationbecause_____________________________________________

4. Translations,rotations,andreflectionsarerigidmotiontransformationsbecause_________________________________________________________________________________________________________________

SET

Topic:Solvingformissingangles

Usewhatyouknowaboutverticalangles,exteriorangles,andtheanglesformedbyparallellinesandtransversalstofindthevalueofxineachofthediagrams.

5. 6.

READY, SET, GO! Name Period Date

Page 41

congruent paralleleverypointis translatedthesamedistanceand direction

perpendicularbisectorcorrespondingpoints areequidistantfromthelineofreflection

distance theymovealongconcentriccircles

theymaintain congruence betweenpreimageand image

X 23185 Xt87 13587 87

X1080 x 48

SECONDARY MATH II // MODULE 5

GEOMETRIC FIGURES – 5.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.6

Needhelp?Visitwww.rsgsupport.org

7. 8.

Proveeachofthefollowing.

9. Given:!isthemidpointof!" !"# !".Prove: ∆!"# ≅ ∆!"#

10. Given∠! ≅ ∠!and!" ≅ !".Prove: ∆!"# ≅ ∆!"#

Page 42

att ext is1150 are I650

75 2 768 211340

xrn xDi r e

srsryfisfznigdffwmtca.vecr wlst vT Given

wyzyypefofmidPOMITW.amEYw EY µIr aMidf

nasrt wT

DVYw D2yxSAS

SECONDARY MATH II // MODULE 5

GEOMETRIC FIGURES – 5.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

5.6

Needhelp?Visitwww.rsgsupport.org

GO

Topic:ConnectingapiecewisedefinedequationwiththecorrespondingabsolutevalueequationThegraphofanabsolutevaluefunctionisgiven.A)Writetheequationusingabsolutevaluenotation.B)Thenwritetheequationasapiecewisedefinedfunction.

15.

A.

B.

16.

A.

B.

17.

A.

B.

18.

A.

B.

2

–2

–4

–10 –5

Page 43

Ix Itt 2 IxH2

txt31 txt 5 4