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85TrapezoidsandKitescomplete.notebook
1
November19,2014
85TrapezoidsandKitescomplete.notebook
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November19,2014
Rememberconsecutiveinteriorangles
aresupplementary.
isoscelesTrapezoid baseangles
baseangles
baseanglesareattachedtothebases.
85TrapezoidsandKitescomplete.notebook
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November19,2014
Theorem8.14
Theorem8.15
Theorem8.16
85TrapezoidsandKitescomplete.notebook
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November19,2014
Answersareonthenextpage.Gotonextpageafteryouhavetakenaminutetofindthemissingangles.
85TrapezoidsandKitescomplete.notebook
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November19,2014
50
130 130
baseanglesarecongruentsotheotherbaseangleis50.Theotherpairofbaseanglesare130,duetoconsecutiveinterioranglestheorem,andbaseanglesarecongruentinanisoscelestrapezoid.
baseanglesarecongruentsotheotherbaseangleis100.Theotherpairofbaseanglesare80,duetoconsecutiveinterioranglestheorem,andbaseanglesarecongruentinanisoscelestrapezoid.
10080
80
85TrapezoidsandKitescomplete.notebook
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November19,2014
Abetterversionofthisformulais:midsegment= base+base
2thinkofthisequationasaproportionandcrossmultiplytosolve.
Anotherwaytorememberthisformulaistothinkofamidsegmentasanaverageofthebases.
Theorem8.17
85TrapezoidsandKitescomplete.notebook
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trytheseproblems,givethemafewminutestopracticeandthenchangethepagetoseetheanswers.
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November19,2014
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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November19,2014
Theorem8.18
Theorem8.19
Howdoyouknowwhichangle?Itistheanglelocatedbetweenthenoncongruentsides.
85TrapezoidsandKitescomplete.notebook
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Givethestudentsafewminutestofindthesolutionstosolvetheproblems.Thenchangethepagetochecktheanswers.
85TrapezoidsandKitescomplete.notebook
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November19,2014
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
85TrapezoidsandKitescomplete.notebook
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November19,2014
Givethestudentsafewminutestotryandfindthemissingsidelengths.Oncetheyarereadymovetothenextpage.
85TrapezoidsandKitescomplete.notebook
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November19,2014
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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November19,2014
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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November19,2014
85TrapezoidsandKitescomplete.notebook
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November19,2014
thediagonalthatgoesthroughthecongruentanglesisbisected.Soonly1diagonalisbisected.
1pairofanglesarebisected.Thepairofnoncongruentanglesarebisected.
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November19,2014
Thehomeworkfromthedayofthetest.
Toprovearectangleonacoordinateplane.Firstfindtheslopeofeachside.Oncethatisdone,thencomparetheslopesandseeiftheslopesareoppositereciprocals,whichwouldmakethesidesperpendicular.Youcanalsoprovethefigureisaparallelogram,andthenfindthelengthofthediagonals.Ifthefigureisaparallelogramwithcongruentdiagonals,thenitisarectangle.
Toproveafigureisasquareyouhavetodoboththerectangleandtherhombus.
Toproveakite,findthelengthofeachsideandfollowthedefinitiontoprovethefigureisakite.
Toprovearhombusonacoordinateplane.Firstfindthelengthofeachside.Oncethatisdone,comparethesidelengths,iftheyareallcongruent,thenthefigureisarhombus.
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