10.4 inscribed angles and polygons - wordpress.com · 6/10/2018  · intercepted arc: an arc that...

10.4InscribedAnglesandPolygonsWhatisaninscribedangle?Inscribedangle:ananglewhosevertexisonacircleandwhosesidescontainchordsofthecircleWhatisthedifferencebetweenaninscribedangleandacentralangle?InterceptedArc:anarcthatliesbetweentwolines,rays,orsegmentsTheorem:MeasureofanInscribedAngleTheoremThemeasureofaninscribedangleisone-halfthemeasureofitsinterceptsarc.Example1:UsingInscribedAnglesFindtheindicatedmeasure

a) !∠#=_________

b) measureofarcQR=_________Example2:FindingtheMeasureofanInterceptedArcFindthemeasureofarcRSand!∠$#%.Whatdoyounoticeabout∠$#%and∠%&$Theorem:InscribedAnglesofaCircleTheoremIftwoinscribedanglesofacircleinterceptthesamearc,thentheanglesarecongruent.Example3:FindingtheMeasureofanAngleGiven!∠' = 75+,find!∠,.

Tryonyourown:Determinethemeasureoftheredarcorangle.InscribedPolygons:ApolygonIsaninscribedpolygonwhenallitsverticeslieonacircle.Example4:UsingInscribedPolygonsFindthevalueofeachvariable:Tryonyourown:Findthevalueofeachvariable.Homework:3-15odd,19-21,25-30,41**