Trapezoids and Kites Complete

85TrapezoidsandKitescomplete.notebook

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November19,2014

85TrapezoidsandKitescomplete.notebook

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Rememberconsecutiveinteriorangles

aresupplementary.

isoscelesTrapezoid baseangles

baseangles

baseanglesareattachedtothebases.

85TrapezoidsandKitescomplete.notebook

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Theorem8.14

Theorem8.15

Theorem8.16

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Answersareonthenextpage.Gotonextpageafteryouhavetakenaminutetofindthemissingangles.

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50

130 130

baseanglesarecongruentsotheotherbaseangleis50.Theotherpairofbaseanglesare130,duetoconsecutiveinterioranglestheorem,andbaseanglesarecongruentinanisoscelestrapezoid.

baseanglesarecongruentsotheotherbaseangleis100.Theotherpairofbaseanglesare80,duetoconsecutiveinterioranglestheorem,andbaseanglesarecongruentinanisoscelestrapezoid.

10080

80

85TrapezoidsandKitescomplete.notebook

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Abetterversionofthisformulais:midsegment= base+base

2thinkofthisequationasaproportionandcrossmultiplytosolve.

Anotherwaytorememberthisformulaistothinkofamidsegmentasanaverageofthebases.

Theorem8.17

85TrapezoidsandKitescomplete.notebook

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trytheseproblems,givethemafewminutestopracticeandthenchangethepagetoseetheanswers.

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x

x=18+102

x=14

7=10+2x210+2x=14

x=2

12.5= 3x+1+152

3x+16=253x=9

x=3

85TrapezoidsandKitescomplete.notebook

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Theorem8.18

Theorem8.19

Howdoyouknowwhichangle?Itistheanglelocatedbetweenthenoncongruentsides.

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Givethestudentsafewminutestofindthesolutionstosolvetheproblems.Thenchangethepagetochecktheanswers.

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Sincethefigureisakitewhichisatypeofquadrilateral,thenthe2anglesthataremissingarethecongruentangles.Therefore100+40=140.360140=220,then220/2=110.Sothetwoanglesareequalto110degreeseach.

Sincethefigureisakitewhichisatypeofquadrilateral,thenIknowthatthemissingangleatthetopis110.Thisisbecuase1pairofanglesarecongruentinakite.NextIaddtheanglesknow,60+110+110=280.360280=80.Sothemissingangleis80degrees.

110

110

11080

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Givethestudentsafewminutestotryandfindthemissingsidelengths.Oncetheyarereadymovetothenextpage.

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x y

Tofindx:

42+62=x2

52=x2

213=x

Tofindy:

62+122=y2

180=y2

920=y

945=y

65=y

85TrapezoidsandKitescomplete.notebook

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m=13

m=13

m=42

2

m=2

4

1

2=

=

Firstfindtheslopeofallsides.SecondyoucansayABllCD,andADllBC.ThismakesthefigureaTrapezoid.ButyouneedtochecktoseeifitisanisoscelesTrapezoid.Thisrequirescheckingtoseeifthelegsarecongruent.UsePythagreanTheorem.

AB

C

D

42+22=AD2

25=AD

and

42+22=BC2

25=BC

Sosincethelegsarecongruent,thenthisfigureisanisosceleTrapezoid.

85TrapezoidsandKitescomplete.notebook

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thediagonalthatgoesthroughthecongruentanglesisbisected.Soonly1diagonalisbisected.

1pairofanglesarebisected.Thepairofnoncongruentanglesarebisected.

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Thehomeworkfromthedayofthetest.

Toprovearectangleonacoordinateplane.Firstfindtheslopeofeachside.Oncethatisdone,thencomparetheslopesandseeiftheslopesareoppositereciprocals,whichwouldmakethesidesperpendicular.Youcanalsoprovethefigureisaparallelogram,andthenfindthelengthofthediagonals.Ifthefigureisaparallelogramwithcongruentdiagonals,thenitisarectangle.

Toproveafigureisasquareyouhavetodoboththerectangleandtherhombus.

Toproveakite,findthelengthofeachsideandfollowthedefinitiontoprovethefigureisakite.

Toprovearhombusonacoordinateplane.Firstfindthelengthofeachside.Oncethatisdone,comparethesidelengths,iftheyareallcongruent,thenthefigureisarhombus.

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