Chapter8Similarity

8.1SimilarPolygonsRecall:Whatdoesitmeanfortwoormoreobjectstobesimilar?SpiralReview:DilatetriangleABC,! 0,0 , $ 0,3 , &(4,0)byascalefactoror2Whatdoyounoticeabouttheangles?Whatdoyounoticeaboutthesides?Example1:UsingSimilarityStatementsInthediagram∆+,-~∆/01,.

a) Findthescalefactorfrom∆+,-34∆/01.

b) Listallpairsofcongruentangles.

c) WritetheratiosofthecorrespondingsidelengthsTryonyourown:

Example2:FindingaCorrespondingLengthInthediagram,∆567~∆89:.FindthevalueofxExample3:FindingaCorrespondingLength.Inthediagram,∆-:+~∆/:1FindthelengthofthealtitudePS.

AreaandPerimeterofSimilarFigures

ThinkbacktotheSpiralReviewproblem.

Whatistheperimeteroftheoriginalfigure?Whatistheperimeteroftheimage?Whatistheareaoftheoriginalfigure?Whatistheareaoftheimage?

Whatcanyouconclude?

Example4:ModelingwithMathematicsBergenCommunityCollegeplanstobuildanewswimmingpool.AnOlympicpoolisrectangularwithalengthof50mandawidthof25m.ThenewpoolwillbesimilarinshapetoanOlympicpoolbutwillhavealengthof40m.FindtheperimetersofanOlympicpoolandthenewpool.Example5:FindingAreasofSimilarPolygonsInthediagram,∆!$&~∆56.Findtheareaof∆567

Example6:DecidingWhetherPolygonsAreSimilar.DecidewhetherABCDEandKLQRParesimilar.Explainyourreasoning.Homework:3,5,7,10,12,13,16,19,20,25,26,27,28-34,51