Name:___________________________________ Math______,Period_____________Mr.Rogove Date:_______________

G8M7L12:ApplicationsofthePythagoreanTheorem1

Learning Objective:WewillapplythePythagoreanTheoremtorealworldandmathproblems.(G8M7L12)Concept Development: TriangleRefreshers:PythagoreanTheorem:Inarighttriangle,thesumofthesquaresofthelegsisequaltothesquareofthehypotenuse.Thisisnotedbytheequation!! + !! = !!where! and !arelegs,andcisthehypotenuse.Areaofatriangle:theareaofatriangleis!! !"#$ × ℎ!!"ℎ!.Theperimeterofatriangleisthesumofthelengthsofthethreesides.Guided Practice: StepsforSolvingProblemsUsingthePythagoreanTheorem1.Readtheproblemcarefullyandidentifythegiveninformationandthemissinginformation.2.Ifnecessary/helpful,drawapicture.3.Setupanequationtohelpyoufindthemissinginformation.4.Solveyourequationandinterprettheanswerinthecontextoftheproblem.Theareaoftherighttrianglebelowis66.5 !!!.Findtheheightandtheperimeter.

Theequilateraltrianglebelowhasasidelengthof4 !!.Findtheheightofthetriangleandthearea.

9.5cm2mm

4mm4mm

2mm

Name:___________________________________ Math______,Period_____________Mr.Rogove Date:_______________

G8M7L12:ApplicationsofthePythagoreanTheorem2

Manytelevisions(andotherdevicesthathavescreens)haveratiosoflengthtowidthof4:3.Forexample,aphonethathasalengthof4inchesandawidthof3incheshasadiagonallengthof5inches(because4! + 3! = 5!).Whenwetalkaboutthesizeofdeviceswithscreens,itisthediagonallengthwearetalkingabout.Howbigisatabletscreenthathasalengthof8inchesandawidthof8inches?

HowbigisaTVthathasalengthof38inchesandawidthof28.5inches(assumea4:3ratio)?

TheTVatthefrontoftheroomalsohasa4:3ratio.Ourtechfolkstoldmeitisa75inchTV.WhatisthelengthandwidthoftheTV?

TheiPhone6Plusalsohasa4:3ratioisbilledashavinga5.5inchscreen.Whatisthelengthandwidthofthescreen?

Name:___________________________________ Math______,Period_____________Mr.Rogove Date:_______________

G8M7L12:ApplicationsofthePythagoreanTheorem3

TherearetwowaystogetfromJames’housetoSarah’shouse.Howlongiseachroute?HowmuchshorteristhediagonalCStreetroute?

InManhattan,Broadwayrunsdiagonallyontheupperwestside.InordertogetfromLincolnCentertoColumbusSquare,youcaneithertakeColumbusAvenuefrom66thStreetSouthto59thStreet(thisis0.4miles)andmakealeftandwalkoneblock(0.3miles),oryoucanjusttakeBroadway.HowfarisitifyoujusttakeBroadway?

Name:___________________________________ Math______,Period_____________Mr.Rogove Date:_______________

G8M7L12:ApplicationsofthePythagoreanTheorem4

Independent Practice: MaybeexercisesfromLesson18(nottheproblemset,butexercises).Activating Prior Knowledge: Closure: LincolnCenterQuestioncanbeclosure.Notes: This is from Lesson 18, Module 7, Grade 8