Unit 9 Circles Notes - Geometry with Mrs. Henry · Geometry Unit 9 Circles 8 Guided Practice 2...
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Geometry Unit 9 Circles 1 Date Lesson Name Days Suggested Get Ready for Chapter 9 1 9.1 Circles and Circumference 1 9.2 Measuring Angles and Arcs 1 9.3 Arcs and Chords 1 9.4 Inscribed Angles 1.5 Quiz 0.5 9.5 Tangents 1 9.6 Secants, Tangents and Angle Measures 2 Review 1 Test 1 Total 11
Transcript of Unit 9 Circles Notes - Geometry with Mrs. Henry · Geometry Unit 9 Circles 8 Guided Practice 2...
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Date LessonName DaysSuggested
GetReadyforChapter9 1
9.1CirclesandCircumference 1
9.2MeasuringAnglesandArcs 1
9.3ArcsandChords 1
9.4InscribedAngles 1.5
Quiz 0.5
9.5Tangents 1
9.6Secants,TangentsandAngleMeasures 2
Review 1
Test 1
Total 11
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9.1CirclesandCircumference
Example1IdentifySegmentsinaCircleA.Namethecircleandidentifyaradius. B.Identifyachordandadiameterofthecircle.
GuidedPractice1A.Namethecircleandidentifyaradius. B.Whichsegmentisnotachord?
a. 𝐴𝑇b. 𝐶𝑇c. 𝐹𝑁d. 𝑇𝑁
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Example2FindRadiusandDiameter GuidedPractice2IfRT=21cm,whatisthelengthofQV? IfQS=26cm,whatisthelengthofRV?
Example3FindMeasuresinIntersectingCircles
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GuidedPractice3
Example4FindCircumferenceCROPCIRCLESAseriesofcropcircleswasdiscoveredinAlberta,Canada,onSeptember4,1999.Thelargestofthethreecircleshadaradiusof30feet.Finditscircumference.GuidedPractice4TheUnisphereisagiantsteelglobethatsitsinFlushingMeadows-CoronaParkinQueens,NewYork.Ithasadiameterof120feet.Finditscircumference.
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Example5FindDiameterandRadiusFindthediameterandtheradiusofacircletothenearesthundredthifthecircumferenceofthecircleis65.4feet.GuidedPractice5Findtheradiusofacircletothenearesthundredthifitscircumferenceis16.8meters.Example6CircumferenceofCircumscribedPolygon
GuidedPractice6
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9.2MeasuringAnglesandArcs
Example1FindMeasuresofCentralAngles GuidedPractice1Findthevalueofx. Findthevalueofx.
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Example2ClassifyArcsandFindArcMeasures
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GuidedPractice2
Example3FindArcMeasuresinCircleGraphs
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GuidedPractice3
Example4UseArcAdditiontoFindMeasuresofArcs
GuidedPractice4
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Example5FindArcLength
GuidedPractice5
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9.3ArcsandChords
Example1UseCongruentChords GuidedPractice1toFindArcMeasureJEWELRYAcircularpieceofjadeishungfromachainbytwowireswrappedaroundthestone.JM≅KLand𝑚𝐾𝐿 = 90.Find𝑚𝐽𝑀.
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Example2UseCongruentArcstoFindChordLengths
GuidedPractice2
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Example3UseaRadiusPerpendiculartoaChord GuidedPractice3
Example4UseaDiameterPerpendiculartoaChordCERAMICTILEIntheceramicsteppingstonebelow,diameterABis18incheslongandchordEFis8incheslong.FindCD.
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GuidedPractice4Inthecirclebelow,diameterQSis14incheslongandchordRTis10incheslong.FindVU.
Example5ChordsEquidistantfromCenter GuidedPractice5
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9.4InscribedAngles
Example1UseInscribedAnglestoFindMeasuresA.Findm∠X.
B.Find
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GuidedPractice1A.Findm∠C.
B.Find
Example2UseInscribedAnglestoFindMeasures GuidedPractice2ALGEBRAFindm∠R. ALGEBRAFindm∠I.
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Example3UseInscribedAnglesinProofs
Statements Reasons
1. 1.Given
2.𝐿𝑂 ≅ 𝑀𝑁 2.Ifminorarcsarecongruent,thencorrespondingchordsarecongruent.
3.< 𝑀intercepts and< 𝐿intercepts . 3.Definitionofinterceptedarc
4.___________________________________ 4.Inscribedanglesofthesamearcarecongruent.
5.∠MPN≅∠OPL 5.VerticalAnglesarecongruent.
6.ΔMNP≅ΔLOP 6.____________________________________
Write a two-column proof.
Given:
Prove: ΔMNP ≅ ΔLOP
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GuidedPractice3
Statements Reasons
1. 1.Given
2.𝐴𝐵 ≅ 𝐷𝐶 2.Ifminorarcsarecongruent,thencorrespondingchordsarecongruent.
3.< 𝐷intercepts and< 𝐴intercepts . 3.Definitionofinterceptedarc
4.∠D≅∠A 4.Inscribedanglesofthesamearcarecongruent.
5.∠DEC≅∠BEA 5.VerticalAnglesarecongruent.
6.ΔDCE≅ΔABE 6.____________________________________
Write a two-column proof.
Given:
Prove: ΔABE ≅ ΔDCE
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Example4FindAngleMeasuresinInscribed GuidedPractice4Triangles ALGEBRAFindm∠D.ALGEBRAFindm∠B.
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Example5FindAngleMeasuresINSIGNIASAninsigniaisanemblemthatsignifiesrank,achievement,membership,andsoon.Theinsigniashownisaquadrilateralinscribedinacircle.Findm∠Sandm∠T.
GuidedPractice5INSIGNIASAninsigniaisanemblemthatsignifiesrank,achievement,membership,andsoon.Theinsigniashownisaquadrilateralinscribedinacircle.Findm∠N.
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9.5TangentsTangentsAtangentisalineinthesameplaneasacirclethatintersectsthecircleinexactlyonepoint,calledthepointoftangency.𝐴𝐵istangentto⊙ 𝐶atpointA.Acommontangentisaline,ray,orsegmentthatistangenttotwocirclesinthesameplane.Ineachfigurebelow,lineℓisacommontangentofcirclesFandG.
Example1IdentifyCommonTangentsA.Drawthecommontangents.Ifnocommon B.Drawthecommontangents.Ifnocommontangentexists,statenocommontangent. tangentexists,statenocommontangent.
GuidedPractice1A.Drawthecommontangentstodeterminehow B.Drawthecommontangentstodeterminehowmanythereare.Ifnocommontangentexists, manythereare.Ifnocommontangentexists,statenocommontangent. statenocommontangent.
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Example2IdentifyaTangent GuidedPractice2
Example3UseaTangenttoFindMissingValues GuidedPractice3
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Example4UseCongruentTangentstoFindMeasures GuidedPractice4
Example5FindMeasuresinCircumscribedPolygons
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GuidedPractice5
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9.6Secants,TangentsandAngleMeasures
Example1UseIntersectingChordsorSecantsA.Findx. B.Findx. C.Findx.
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GuidedPractice1A.Findx. B.Findx. C.Findx.
Example2UseIntersectingSecantsandTangents
A.Findm∠QPS. B.Find
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GuidedPractice2A.Findm∠FGI. B.Find
Example3UseTangentsandSecantsThatIntersectOutsideaCircleA.Find B.Find
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GuidedPractice3A.Find B.Find
Example4ApplyPropertiesofIntersectingSecants
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GuidedPractice4
