Activity #3 - Google Sites · p164 #15 OYO p179 #1 p180 ... Foldable Properties, ... "I use the Law of Sines when I know SAA or SSA."

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Activity#3Howmanythingsaregoingoninthissimpleconfiguration?

WhenyourTEAMhas10ormorethings,getALLofyourstuffstampedoff!

EO2Level2AnswersID:AID:B

F

H

CompleteMRforLevel3'sonly 2availableAcademicSupportPeriods

Turnitin(staplecherryformontopofyourcorrections/workandputthetestintheback)

Ifyouare100%correctontheMasteryReform,youareeligiblefortheretake.

EveryonetakingtheretakemustcompleteboththeLevel3andLevel4sections Dobetter?Lowergradeisdropped

Doworse?Level3scoresareaveragedandthelowerLevel4scoreisdropped

MasteryReform

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Level2Opp#2

EO1OneVariableInequalities 12%

EO2TwoVariableInequalities 13%

EO3Similarity&Congruence 25%

EO4Polynomials 25%

Q3Midterm

EO1Level3Mastery

ReformDueMon,Jan30th

EO1Opp#1Thu,Jan19th

EO1Opp#2Tue,Jan31st@B211

EO2Level3Mastery

ReformDueTue,Feb7th

EO2Opp#2Thu,Feb9th

EO3Level3Mastery

ReformDueFri,Feb24th

EO3Opp#2Tue,Feb28th

Q3FinalFri,March10th

EO2Opp#1Fri,Jan27th

EO3Opp#1Tue,Feb14th

EO4Opp#1Wed,Mar8th

ML

Math3Quarter3Overview

MLML

130 131 21 22 23

SignedProgressReportduelastFriday!

p163TATSInv311Inv311p164#15

OYOp179#1p180#3

PropertiesofSimilarPolygons(basedonInv1#5)

p167STM,CYU,EQ

OYOp40#1,p43#9

AngleVocabularyParallelLinesCut

byaTransversalFoldable

Properties,Postulates,&Theorems

Inv121p30#13,EQ

Similarity&ProportionPractice

Inv312p168#15,STM,CYU,EQ

Inv313p175#3,4,5***,6

OYOp41#3,5p45#13*,

p46#14,15**

OYOp180181#4Writeproofs!

*p45#13AngleAdditionPostulate

**p46#15ExteriorAngleTheoremforaTriangle

***p176#5MidpointConnectorTheoremforTriangles

EO1Opp#2Tue,Jan31st

SolvinganSASTriangle

SimilarityTheorems

TipsforWritingSimilarityProofs

EO2MasteryReformdueTuesday

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26 27 28 29 210

Inv322p202#4STM,CYU,EQ(organizer)

TriangleCenters(handout)

TipsforCongruenceWritingProofs

TriangleCenters

PropertiesofQuadrilaterals

ProofsInvolvingSimilarTriangles

TriangleCongruenceFlipBook

p195TATSInv321p196#24,67,STM,CYU,EQ

EO3Quiz#2Fri,Feb10thEO3Quiz#1

Mon,Feb6th

TeamHomeworkDiscussion OYOp27#31,p125126#30

OYOp179#1,p180#3

Similarity&ProportionPractice

OYOp40#1,p43#9

OYOp41#3,5,p45#13*,p46#14,15**

Fullcredit(2stamps)beforeteamdiscussion.Partialcreditafter.

AnswersinslidesjustbeforeToolkitentries.

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p168

EssentialQuestionsWhatcombinationsofsideoranglemeasuresaresufficientto

determinethattwotrianglesaresimilar?

LanguageObjectiveMathematicianswillbeableto......useAA,SSS,andSAStoprove2trianglessimilar.

Activities#15,STM,CYU,EQ

p168

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GivenSAS

information

UsetheLawOfCosinestofindthe3rdside

UseLawOfSinestofindthe2ndangle

UsetheTriangleSumPropertytofindthe3rdangle

TOOLKIT:SolvingaSAStriangleReference:Investigation2SufficientConditionsforSimilarityofTrianglesp169#1

Example: UsetheLawOfCosinestofindthe3rdside



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2m 4m

Couldyousaythetrianglesweresimilar?

3m 6m83o

83o

SideAngleSidesimilaritytheorem!

Ifyousawthis:

17m

51m


10m 15m 30m 45m

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LawofCosines

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17m

51m


10m 15m 30m 45m

SideSideSidesimilaritytheorem!

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#2SSSSimilarityTheorem!

TOOLKIT:SimilarityTheorems#1SASSimilarityTheorem!

#3AASimilarityTheorem!

NOTE:WhyareASAandSAAnotincludedassimilaritytheorems???

ANSWER:Whenconsidering"sufficientconditions"wearelookingfortheminimumcriteriathatconsistentlyprovessimilarity.SincewehaveprovedAAasasimilaritytheorem,that'stheminimumcriteria.BothASAandSAAaddanadditionalcriteriaofaS(side).CanyouseethatbothASAandSAAhaveAAinthem?

SSS~Thm

SAS~Thm

AA~Thm

Whatissufficientinformation?Correspondencepatternsthatworkforsimilarity:

SAS SSS AA

p172

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p172

57o38o

57o

95o

28o

85o

Similar? NO!

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35o

Similar? YES!

35o

12

15

16

20

Similar? YES!

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Similar? NO!

416

18

1040

48

12

1263o

83o

63o34o

83o34o

Similar? YES!

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Math1

TOOLKITS

TOOLKIT:PythagoreanTheorem&ItsConverse

ThePythagoreanTheoremcanbeusedtofindanymissingsideofaRIGHTtrianglesolongastwosidesofthetriangleareknown.

Examples:

Findthehypotenuse:

Findtheleg:

TheConverseofthePythagoreanTheorem:Foraanytrianglewithsidesa,b,c,ifa2+b2=c2,thenit'sarighttriangle

1.Writea2+b2=c22.Fillinthe3partsthataregiventoyou.

Makesuretheygointherightspot!cisalwaysthelongestside.3.Solveeachsideoftheequation.

Ifequal,thenit'sarighttriangle.IfNOTequal,thenit'sNOTarighttriangle

4.Writeyouranswerinacompletesentence

?

1.Writea2+b2=c2

2.Fillinthe3partsthataregiventoyou.

Makesuretheygointherightspot!cisalwaysthelongestside.

3.Solveeachsideoftheequation.Ifequal,thenit'sarighttriangle.IfNOTequal,thenit'sNOTarighttriangle


?

5in

12in13in

Example#1 1.Writea2+b2=c2

2.Fillinthe3partsthataregiventoyou.

Makesuretheygointherightspot!cisalwaysthelongestside.

3.Solveeachsideoftheequation.Ifequal,thenit'sarighttriangle.IfNOTequal,thenit'sNOTarighttriangle


?

3cm5cm

7cm

Example#2

Askingthequestion"Isittrue?"

ThePythagoreanTheorem:Forarighttriangle,thesumofthetwoleglengthssquaredisequaltothelengthofthehypotenusesquared.

a

b

c

a2+b2=c2

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TOOLKIT:TriangleInequalityTheorem

Thesumofanytwosidelengthsofatriangleisgreaterthanthethirdsidelength.

ac

b

Examples:

Activity#2:Canthesesidelengthsformatriangle?Quadrilateral?Explain.

1) 5,7,13

2) 6,12,9

3) 25,10,15

4) 3,5,7,13

5) 12,6,9,25

6) 24,2,14,8

TOOLKIT:QuadrilateralInequalityTheoremThesumofanythreesidelengthsofaquadrilateralisgreaterthanthefourthsidelength.

ac

b

dExamples:

45

8

7

2 35

12Canformaquadrilateral

Cannotformaquadrilateral

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TOOLKIT:TriangleCongruencyTheorems

S.A.S.S.S.S.A.A.S.A.S.A.H.L

S.S.A A.A.A

So,howmanycombinationsofanglesandsidesarepossible?Six!

ButtwoofthemcanNEVERbeusedtoprovecongruence.

Becarefultorecognizethattheorderoftheselettersrepresentstheshortestconsecutivepatharoundthetriangle.Doyouunderstand???

CONGRUENTFIGURESAllcorrespondingsides

andallcorrespondinganglesarecongruent(equal)!

So,itmustbearighttriangletohaveanhypotenuse!

Triangleshave3anglesand3sidelengths.Toprovethattrianglesarecongruent,youmustshowthatthereare3congruentparts.

AB DE XYAC DF XZBC EF YZ

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TOOLKIT:CorrespondingPartsofCongruentTrianglesareCongruent

(CPCTC)

CPCTC:CorrespondingPartsofCongruentTriangles

areCongruent

Whendevelopingaprooffortriangleparts,youmustfirstprovethatthetrianglesarecongruent,andthenyoucanuseCPCTCasthereasonthetriangle'sotherpartsarecongruent.

Besurethatyouunderstandeachpartofthisstatement.

TriangleSumProperty

Thesumofallanglesofatriangleisequalto180o

A

BC

Ifthevalueof2quantitiesareknowntobeequal,thenthevalueofonequantitycanbereplacedbythevalueoftheother.

Subtractingthesamenumberfromeachsideofanequationgivesusanequivalentequation.

Whentwolinesintersect,oppositeanglesthatsharethesamevertexorcornerpointarecongruent.

ReflexiveProperty

Congruenttoitself(appliestobothsegmentslengthsandangles)

sharedline

D

A

C

B

VerticalAnglesTheorem

SubstitutionPropertyofEquality

A

B

C

DE

sharedangle

SubtractionPropertyofEquality

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TOOLKIT:LawofSines

"IusetheLawofSineswhenIknowSAAorSSA."

SetUpTips1.Beginwiththefractionbars&equalsign2.Putyourunknowninthefirstnumerator3.Puttheoppositeterminthedenominator4.Puttheknownangle&oppositesidepairontheright

or

Side

Angle Angle

Side,Angle,Angle

Side

SideAngle

Side,Side,AngleInbothcasesIknow1angle&oppositesidepair!

Math2

TOOLKITS

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a

b

c

A

B

C

TOOLKIT:PythagoreanTheorem

Whensolvingforthehypotenuse:Whensolvingforoneofthelegs:

Ifthesquareofonesideofatriangleisequaltothesumofthesquaresoftheothertwosides,thenthetriangleisarighttriangle.

PythagoreanTheoremConverse

3,4,5 5,12,13 8,15,17

TherearecertainsetsofnumbersthathaveaveryspecialpropertyinconnectiontothePythagoreanTheorem.NotonlydothesenumberssatisfythePythagoreanTheorem,butanymultiplesofthesenumbersalsosatisfythePythagoreanTheorem.

PythagoreanTriples:

TOOLKIT:StandardPositionAngle

InitialSide

TerminalSide

66o

Anangleformedbyrotating(counterclockwiseispositive,clockwiseisnegative)arayfromitsinitialposition(vertexattheoriginandlayingonthexaxis)totheterminalposition.

y

x66o

P(x,y)Foranystandardpositionanglewhoseterminalsidepassesthroughthepoint(x,y),weknowthe3sidelengthsare...

x

y

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y

P(x,y)

Hypotenuse

Opposite

Adjacentx

TOOLKIT:TrigFunctions:Sine,Cosine,andTangentyrsin==

Opposite

Hypotenuse

xrcos==

AdjacentHypotenuse

yxtan==

Opposite

Adjacent

SohCahToaMemorize! NotetoStudents:This

Toolkitissufficientbyitself,butyoucanalsoaddthenext3slidesifyouwant.

TOOLKIT:InverseTrigFunctions

Anytimewe'resolvingfortheANGLEweusetheINVERSEtrigonometryfunction.

Taketheinversetrigfunctionofeachsideoftheequation

Anyvaluetimesitsinverseequals1

Useyourcalculator(inDEGREEmode)tofindtheanswer

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TOOLKIT:"Special"RightTrianglesTherearetwo"special"righttriangleswithwhichyouneedtobefamiliarthe454590triangleandthe306090triangle.The"special"natureofthesetrianglesistheirabilitytoyieldexactanswersinsteadofdecimalapproximationswhendealingwithtrigonometricfunctions.

Thischartshowsthevalueswithrationalizeddenominatorsaswellasthe123and321tricktohelpthosestudentswholikememorizingtables.

Whenyouthenrationalizethedenominator,you'llget

TOOLKIT:AnglesElevation&Depression

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TOOLKIT:LawofSines ,Part1

or


InbothcasesIknow1angle&oppositesidepair!

TOOLKIT:LawofSines ,Part2


SetUpTips1.Beginwiththefractionbars&equalsign2.Putyourunknowninthefirstnumerator3.Puttheoppositeterminthedenominator4.Puttheknownangle&oppositesidepairontheright

or

Side

Angle Angle

Side,Angle,Angle

Side

SideAngle

Side,Side,AngleInbothcasesIknow1angle&oppositesidepair!

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GivenSASinformation

UseLOCtofindthe3rdside

UseLOStofindthe2ndangle


TOOLKIT:LawofCosines(LoC)

SolvingaSASTriangle:

SolvingaSSSTriangle:

GivenSSSinformation

UseLoCtofindoneangle

UseLoStofinda2ndangle


Solvingforthe3rdsidewhengivenSAS

Solvingforthe1stanglewhengivenSSS

Equal,EquivalentForms

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TOOLKIT:MidpointConnectorTheoremforTriangles.

Ifalinesegmentjoinsthemidpointsoftwosidesofatriangle,thenitishalfthelengthofthethirdsideofthetriangleand

paralleltothethirdside.

MN||AC2MN=AC

EO3TOOLKITSSimilarity

Math3

CalculatingScaleFactors

PropertiesofSimilarPolygons(seeInv1#5slides)

ParallelLinesCutbyaTransversalFoldable

ParallelLinesCutbyaTransversalProperties

Properties,Postulates,&Theorems

AngleDefinitions

SolvingaSASTriangle

SimilarityTheorems

TipsforWritingSimilarityProofs

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TOOLKIT:CalculatingScaleFactors

sidelengthofthelargerpolygonsidelengthofthesmallerpolygon=Smallertolargerpolygon

sidelengthofthesmallerpolygonsidelengthofthelargerpolygon=Largertosmallerpolygon

ScaleFactor>1

ScaleFactor

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TOOLKIT:ParallelLinesCutbyaTransversal

FOLDABLE

LinearPairPostulate

VerticalAnglesTheorem

AngleAdditionPostulateSeep45#13

MidpointConnectorTheoremforTrianglesSeep176#5

SubstitutionPropertyofEquality

Addition,Subtraction,MultiplicationorDivisionPropertyofEquality*

Ifthevalueof2quantitiesareknowtobeequal,thenthevalueofonequantitycanbereplacedbythevalueoftheother.

Adding,subtracting,multiplying,ordividing*thesamenumberfromeachsideofanequationgivesusanequivalentequation.

*Pickjustoneoperation!

Twoadjacentangleswhoseunsharedsidesformastraightanglearesupplementary(equalto180o)

180o

Whentwolinesintersect,oppositeanglesthatsharethesamevertexorcornerpointarecongruent.

CorrespondingAnglesPostulate

AlternateInteriorAnglesTheorem

AlternateExteriorAnglesTheorem

SamesideInteriorAnglesTheorem

SamesideExteriorAnglesTheorem

CAsareCongruent

AIAsareCongruent

AEAsareCongruent

SSIAsareSupplementary

SSEAsareSupplementary

Anexteriorangleofatriangleisequaltothesumofthetworemoteinteriorangles

ExteriorAngleTheoremforaTriangleSeep46#15

Reflexiveproperty Congruenttoitself

TOOLKIT:Properties,Postulates,&Theorems

NameDescriptionDiagram

Ifthetwomidpointsofatriangleareconnected,thenthemidlineisparalleltoandhalfthelengthofthethirdside.

IfPisapointintheinteriorofthen

B

AP

C

or

p31

p32

p31

ConverseoftheCorrespondingAnglesPostulate

ConverseoftheAlternateInteriorAnglesTheorem

ConverseoftheAlternateExteriorAnglesTheorem

ConverseoftheSamesideInteriorAnglesTheorem

ConverseoftheSamesideExteriorAnglesTheorem

Iftwolinesareintersectedbyatransversalandcorrespondinganglesarecongruent,thenthelinesareparallel.

Iftwolinesareintersectedbyatransversalandalternateinterioranglesarecongruent,thenthelinesareparallel.

Iftwolinesareintersectedbyatransversalandalternateexterioranglesarecongruent,thenthelinesareparallel.

Iftwolinesareintersectedbyatransversalandsamesideinterioranglesarecongruent,thenthelinesareparallel.

Iftwolinesareintersectedbyatransversalandsamesideexterioranglesarecongruent,thenthelinesareparallel.

NOTE:WewilladdtothisToolkitasnecessary.

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TOOLKIT:AngleVocabularyPoint

Line

Plane

Angle

Right Angle

Obtuse Angle

Acute Angle

Straight Angle

Adjacent Angles

Linear Pair

Vertical Angles

Complementary Angles

Supplementary Angles

Perpendicular LinesParallel Lines

Transversal

Postulate (or axiom)Theorem

NOTE:WewilladdtothisToolkitasnecessary.

|| lines in a plane do not intersect

Define the following terms. Diagrams would be helpful.

Anglescanbenamedwithnumbers.

13

42

WU

V

YX

Notethatisnotspecific.Itcouldbereferringtoanyof4angles.

Anglescanbenamedwithletters.

two rays with a common starting point

identifies a position, has no dimension, labeled with a single capital letter

determined by two points, infinite length, no thickness or width, labeled with two capital letters with a line above or one single lower case letter

a two-dimensional serface determined by 3 points, infinite length and width but no thickness, labeled with 3 capital letters or one italicized capital letter

adjacent angles whose measures add up to 180 degrees (supplementary)

two congruent angles formed by intersecting lines

2 angles whose measures add up to 180 degrees

line that intersects parallel lines

lines in a plane that intersect at 90 degree angles

2 angles whose measures add up to 90 degrees

13

42

equals 90 degrees

greater than 90 degrees

less than 90 degrees

equals 180 degrees

two angles with a common vertex and shared side (ray)

GivenSAS

information

UsetheLawOfCosinestofindthe3rdside



TOOLKIT:SolvingaSAStriangleReference:Investigation2SufficientConditionsforSimilarityofTrianglesp169#1

Example: UsetheLawOfCosinestofindthe3rdside



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SSS~Thm

SAS~Thm

AA~Thm

TOOLKIT:TipsforWritingSimilarityProofs

GIVEN:Couldbeinlist,asentence,oradiagram.PROVE:Typicallyfouroptions Trianglesaresimilar~ Correspondinganglesarecongruent Sidesarerelatedbythesamescalefactor Linesareparallel

STATEMENTREASON

Yourfinalstatementmustbeexactlythesameaswhatyou'reaskedtoproveintheprompt.

Ifprovingthattrianglesaresimilar,thenyourlaststatementisasimilaritystatement

IfprovingthatProvethatcorrespondinganglesarecongruent,thenyourlaststatementisananglecongurencestatement.

Ifprovingthatsidesarerelatedbythesamescalefactor,thenyourlaststatementisascalefactorstatementwherekisthescalefactor.

Ifprovingthatlinesareparallel,thenyourlaststatementisaparallellinesstatement.

Thebodyoftheproofmustleadtothesimilaritytheoremthatyou'reusing:

AA~Thm:Writestatements&reasonsthatshowthatthetwopairsofcorrespondinganglesarecongruent.

SSS~Thm:Writestatements&reasonsthatshowthatallcorrespondingsidesarerelatedbythesamescalefactor.

SAS~Thm:Writestatementsandreasonsthatshowthatthetwopairsofcorrespondingsidesarerelatedbythesamescalefactoreandthattheincludedanglesarecongruent.

1.Proofstypicallybeginbystatingthegiveninformation

1.Given

AA~ThmorSSS~ThmorSAS~Thm

CASTC*(CorrespondingAnglesofSimilarTrianglesareCongruent)

CSSTSSSF*(CorrespondingSidesofSimilarTrianglesSharetheSameScaleFactor)

If......correspondinganglesarecongruent......alternateinterioranglesarecongruent......alternateexterioranglesarecongruent......samesideinterioranglesaresupplementary......samesideexterioranglesaresupplementary...

...thenthetwolinescutbythetransversalareparallel.

Pickthereasonthatfitstheproof

{

*CASTCandCSSTSSSFaretheacronymsforthephrasesinparenthesis.Ifyoucanrecalltheacronymcorrectly,thenuseit.Ifnot,youneedtowriteoutasimilarlywordedreason.

NOTE:Youmusthaveshownthatthetrianglesaresimilarfirst,thenyoucanusethisreason!

NOTE:Youmusthaveshownthatthetrianglesaresimilarfirst,thenyoucanusethisreason!

ConverseoftheCorrespondingAnglesPostulate

ConverseoftheAlternateInteriorAnglesTheorem

ConverseoftheAlternateExteriorAnglesTheorem

ConverseoftheSamesideInteriorAnglesTheorem

ConverseoftheSamesideExteriorAnglesTheorem

Attachments

M3211Organizer.docx

M3311ParallelLines&TransversalFoldable.pdf

SelectorTools.exe

EO2 Inequalities in 1 Variable Name __________________

Unit 2 Lesson 1 With calculator Date: _______________ Period ____

Warm-Up

Match the following number line graphs with the correct symbolic inequality solutions.

1) A)

2) B)

3) C)

4) D)

5) E)

6) F)

Reminders:

7) When you have an open dot (non-filled in circle) you are using the _____ or _____ sign.

8) When you have a closed dot (filled in circle) you are using the _____ or _____ sign.

9) When reading an inequality, like x > 2, it is explaining the answer to some rule of possible x-values that can be plugged in and solve to be true.

a. Therefore, some x-values that do NOT work in the example x > 2 are: __________________________

b. And some x-values that do work in the example x > 2 are: _______________________

c. Can x = 2 here? Why or why not?

Interval Notation: Mathematicians (like yourself) can used interval notation as a kind of shorthand to also describe the solutions like the ones above. Interval notation uses parentheses () and brackets [], like symbolic inequalities and closed and open circles on a number line. Examine the following rules and examples below.

Rules:

When using greater than (>) and less than ( 2

Number Line:

Interval Notation: (2, )

When thinking about Interval Notation, think of it as the range in which all the solutions falls. The parentheses before 2 is telling us that the solutions start as any number larger than 2. The infinity symbol,, is telling us that the solution goes on forever for any number greater than 2. ALL infinity symbols, - or , must have a parentheses next to it since we can never actually reach it.

Example 2: The 3 ways to represent solutions of all x-values less than or equal to -1 or all x-values greater than 2.

Symbolically:

Number Line:

Interval Notation: (, 1] (2, )

The symbol, , means the union of the two intervals. So, the numbers that are in one interval (negative infinity to -1 included) or the numbers in the other interval (any number greater than 2) are the solutions.

Practice writing interval notation from a number line graph: Write the following solutions in interval notation.

1) 2)

3) 4)

Practice writing interval notation from symbolic notation: Write the following solutions in interval notation.

6) 7)

8) 9)

10)

Practice writing solutions symbolically AND on a number line graph when given interval notation:

11) Solution: (, 5]Symbolically:

Number Line:

12) Solution: [, 1)Symbolically:

Number Line:

13) Solution: (, 2) [5, ) Symbolically:

Number Line:

Name: ___________________________ Date: _________________ Period: ____ Page 109

Unit 2 Lesson 1 Investigation 1 Getting the Picture Activities #1-2, STM, CYU, EQ

Essential Questions

Essential Question(s)

Language Objective(s): Mathematicians will be able to

On page 107 of your book:Unit 2: Inequalities and Linear Programing

For some people, athletes and astronauts in particular, selection of a good diet is a carefully planned scientific process. Each person wants maximum performance for minimum cost. The search for an optimum solution is usually constrained by available resources and outcome requirements.

Lesson 1: Inequalities in One Variable

Use numeric and graphic estimation methods and algebraic reasoning to solve problems that involve linear and quadratic inequalities in one variable.

Page 108: Lesson 1 Inequalities in One Variable.

In previous courses, you learned how to solve a variety of problems by representing and reasoning about them with algebraic equations and inequalities. For example, suppose that the plans for a fundraising raffle show that profit P will depend on ticket price x according to the function. A graph of profit as a function of ticket price is shown here.

Page 109: Think About This Situation: Questions important to the fundraising group can be answered by solving inequalities involving the profit function.

a) What would you learn from solutions of the following inequalities?

i.

ii.

iii.

iv.

b) How could you use the graph to estimate solutions of the inequalities in Part a?

c) In what ways could you record solutions of the inequalities in words, symbols, or diagrams?

Page 109-110: In this lesson, you will learn how to use graphical reasoning and algebraic methods to solve inequalities in one and two variables. You will also learn how to represent the solutions symbolically and graphically and how to interpret them in the contexts of the questions that they help to answer.

Investigation 1: Getting the Picture

You learned in earlier work with inequalities that solutions can be found by first solving related equations. For example, in the raffle fundraiser situation, the solutions of the equation

are approximately $1.23 and $5.44. The reasonableness of these solutions can be seen by scanning the graph of the profit function and the constant function y = 2,500. (Hint: Graph -2500+5000x-750x2 in Y1, and Graph 2500 in Y2 of your graphing calculator. Push 2nd, Push Trace, pick 5: Intersect to find the intersection points).

The solution of the inequality are at values of x between $1.23 and $5.44. Those solutions to the inequality can be represented using symbols or a number line graph.

How would you write the solutions to the inequality in interval notation?

Similarly, the solutions of the inequality are all the values of x that are either less than $1.23 or greater than $5.44. Those solutions can also be represented using symbols or a number line graph.

How would you write the solutions to the inequality in interval notation?

As you work on problems of this investigation, look for answers to these questions:

How can you solve inequalities in one variable?

How can you record the solutions in symbolic (inequality), graphic, and interval notation form?

#1) on page 110-111

The next graph shows the height of the main support cable on a suspension bridge. The function defining the curve is . Where x is horizontal distance (in feet) from the left end of the bridge and h(x) is the height (in feet) of the cable above the bridge surface.

a. Where is the bridge cable less than 40 feet above the bridge surface?

Write the equation or inequality that could be used to solve.

Mark/circle the part or parts of the graph that are solutions. (Use your graphing calculator to help you find more exact answers when writing solutions).

Express Solution Symbolically

Express Solution Graphically

Express Solution in Interval Notation

b. Where is the bridge cable at least 60 feet above the bridge surface?






c. How far is the cable above the bridge surface at a point 45 feet from the left end?






d. Where is the cable 80 feet above the bridge surface?






#2) on page 111

The graph below shows the height of a bungee jumpers head above the ground at various times during her ride on the elastic bungee cord. Suppose that h(t) gives height in feet as a function of time in seconds

For each Part a-d:

Write a question about the bungee jump that can be answered by the indicated mathematical operation.

Use the graph to estimate the answer.

Express your answer (where appropriate) with a number line graph and interval notation.

a) Evaluate h(2)

b) Solve h(t) = 10

c) Solve h(t) 10

d) Solve h(t) < 10.

Summarize the Math p111

a.

b.

c.

Check Your Understanding p112

a.

bi.

ii.

iii.

c.

Now answer the Essential Questions.

How can you solve inequalities in one variable?

How can you record the solutions in symbolic, graphic, and interval form?

SMART Notebook

Corresponding s:

Alternate exterior s:

Same side exterior s:

Corresponding s:



Corresponding s:



Corresponding s:



Corresponding s:

Alternate interior s:

Same side interior s:

Corresponding s:



Corresponding s:



Corresponding s:



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Activity #3 - Google Sites · p164 #15 OYO p179 #1 p180 ... Foldable Properties, ... "I use the Law of Sines when I know SAA or SSA."