Which of the following best describes deductive

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□whiehorthe恥oTYhgbestdescribesdedueti、,e
reasoning?
田
theargumentsbelov上
監禁善書
誓書嵩嵩謀 議謹書晋n
A uslngloglCtOdraW′COnCiusionsbasedon
acceptedstatements
B acceptlngthemeanlngOfatem1両thout
de魚nition
I
C de師ngmathematicaltemstocorTeSPOnd
Withphysicalo申ects
CllOne(S),ifan〕′,uSe。eductivereasoning?
DinferTingageneraltnlthbyexamiTmga
Ionly
numbeI’Ofspecificexamples
Honl)′
lSClの)跡
bothIandIJ
neitherInorlI
田Inthediagrambe・ow,,∠1≡∠4.
C湘j父
田 土。「。m:Atriangl。hasatm。=
anh
E。」。。isp.。mgtheth。。remab。V。。,
co五adiction.Hebeganbyassumingthatin
△Abc,∠Aand∠Bareb。th。btuse∴Whi。h
theoremlViIIEduardousctoreacha
i
。。五adi。ti。,1?
A
IfLWOanglesofatriangleareequal,thesides
OPPOSitetheanglesareequal
B
r
IftwosupplementaIyanglesareequal,the
angleseachmeasure900.
C
lVhichofthefbllo、VlngCOnCIusionsdoesnot
Thelargestangleinatriangleisoppositeme
Jongestside.
havetobetrue?
D
A ∠3and∠4aTeSupPlemenar)angles.
Thesumofthemeasuresofdleanglesofa
高angleis1800.
B LineTisparalleltolineI71.
(Sl基調)i!
C ∠1≡∠3
D‘∠2≡∠3
CSGi働
ー 6 −
CALIFORNIA STANDARDSTBST
田UsethepI・00ftoansiYerthequestionbeloW,・
窪
Prol,e:△ABD≡△CBD
Statement
l ︵∠ tJ 4
l. AB≡BC;DisthemidpointofAC
2. AD三三CD
3. BD三三BD
4. △ABD…≡△CBD
。土連理旦
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Propcrty
WThatreasor,LCanbeusedtoprovethattlletrianglesare
B
C
D
AAS ASA SAS SSS
A
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認諾露頭題詞圃題穎園
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A
Ifweassumethatm∠4・=m∠C,itfollovt・stllat
AB=BC・ThiscontradictstlleglVenStatement
thatAB>BC.WhatconclusioneanbedraWn
fromthiseontradiction?
A m∠A二m∠B
B∴∴m∠4≠m∠B
C m∠A二m∠C
D m∠A≠m∠c
c5くす〇万24
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田町setheprooftoanswerthequestionbeloW′・
Gil′en:∠2≡∠3
Prove:∠1≡∠4
t
Statement
l. ∠2≡∠3
2. ∠1≡∠2;∠3竺∠4
3. ∠1≡∠4
Whatreasoncanbeusedtojus憤fystatement2?
A Complementsofcongruentanglesarecongruent.
B、VerticaIanglesarecongmenL
C SupplementsofcongruentanglesareCOngment.
D Correspondinganglesarecongruent.
ba鍵donpc命manceonre庖ゞ鎚le点q嶋高く,時.Copy厘hl④2009C小暗−rnねDcparmenl0「助uc涌on.
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WllichofthefoIIoWlngbestdescribesa
ifaquadrikiteraihasperpendicuIar
COuTZte7”e:rampletotheassertionabove?
diagonais,thenitisarhombus.
A coplanarlines
B parallellines
WI tllfi 土。血。ftll。踊ngisa。。unt。脚。!。t。 istatenlental〕0ヽre?
C perpendicu】arlines
Dintersectlnglines
(=Stmlm
田、唖h聖recanseⅣeaSaCOunterexanlpl。t。
theconJeCturebeloW?
ifonepairofoppositesidesofa
quadriiateralisparal胤,thenthe
quadrilateraIisapara旧ogram.
A rectangle
B rhombus
C square
D 仕apezoid
回
Given:TRAPisanisoscelestrapezoidwith
diagonaIsRPandTA・Wmichofthefbllowfmg
mI∬tbetrue?
A RP⊥コA
B RPliTA
C
T
D
、
ヽ
,
RP三TA
RPbisectsTA
O
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0WTllVOrds.OnestudentWrOtethefbl10Wlng
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triangJesmustbesimilar?
小′00btusetriandes
Statement.
時′oscalenetriangles、涌hcongruentbases
TheareaofaparaILeiogramisthe
t、、′Orighttriangles
PrOductofanybase(b)andanyheight(h).
tW′OisoscelestdanglesWithcongmenL
VeneXangles
叢亜董園田
C
E
A
CEandBEarecongruent.
B
∠ACEisahghtangle.
C
ACandDEareparallel.
D
∠Aand∠Bareeongnent.
baぶed()nPerfommCeOnTelease近喧しque諒ons Copyr−gh!㊧2009
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回para・・elogramABCDissho、Tnb.I。W.
LraWnandintersectatpointM・Whiehof
OIJoIYlngStatementslnlLSEbetrue?
A
AFGImstbeanobtuse血ngle.
△HIGmlStbeanacutetriangle・
△相4cmuStbecongmentto△HMG.
△GMIImustbecollglmenttO△初F.
03 恥te
回
WhichpairoftriangLescanbeestablishedto
Ofthefollo高ngbeStdescribesthe
;SShollmbelolV?
I〕eCOngmenttOpI’0Vethat∠DAB≡/BCD?
A AADCand△BCD
B △AED and△BEC
C △DABand△BCD
D ADECand△BEA
CSG川ilb
回
If△ABCand△XYZaretwotriangIessuch
thatE=若W,hichorthefbuowhgwould
besu餓cienttoprovethetriangIesaresimilar?
A ∠A=∠X
A LOthsimilarandcongrluent
B ∠B≡∠Y
Biimila.。u。n。,。。ngm。nt
C ∠C≡∠Z
c Lngm。n。butn。.Sim血
D ∠X≡∠Y
ithersimilarnorcongruent
CSCi能)も
basedonpedbmanceonre血潮teslq嶋高0踏・Copynghl@料09⊂高車miaDeparim如。「註壷。n.
回whichofth諭lo、Yingstatementsmustbetme
ifAGHII〉△JKL?
回
i)eloW,AC≡DFand∠A≡∠D.
G△:<L
A ThetWOthnglesmustbescalene.
additionalinformationwouIdbeenough
B ThetwotriangiesmusthaveexactlyOneaCute
tobrOVethat△ABC≡△DEF?
angle・
C AtleastolleOfthesidesofthetwotriangles
A
AB≡DE
B
AB=BC
C
BC≡EF
D
BC≡DE
mustbeparallel.
D ThecoITeSPOndingsidesofthetwotIiangles
mustbeproponionaL
CSC;頭rIJ
回ⅥichmethodIistedbelo、VCOuldI20tbeusedto
provethattTYOtrianglesaI’eCOngruent?
A Proveallthreesetsofcorrespondingsides
COngment.
B Proveallthreesetsofcorrespondingangles
COngru nn・
C Provedla白WOSidesandanincludedangleof
Onetrianglearecongruenttotwosidesandan
includedangleoftheohertriangle.
D Provemattwoanglesandanincludedsideof
OnetIianglearecongmenttOtWOanglesand
anincludedsideoftheothertriangle.
CSCIOiji
basedonpe五m肌CeOnrele地溝dt的岬C諒。恥・Copyngh{@2009〇品かmiaD型丁血n国手軸ue壷on.
回
A
B
C
D
basedonpe爪}rmanCeOnでeIe谷eJ誌lqlしe高踏・C・,Pynghi@2009C痛心r胴Dep孤menIor蘭uc証(川.
回、Vhichofthe制owingsetsofnumberscou・d
representthelengthsofthesidesofatriangIe?
回
A 2,2,5
ノ
く J
5
n も 1 1
D
︵′⊃ 4. 5
C
3 4 5
B
国禁祭器慧諾parallellinesl
Whichstatementaboutanglesland2mI‘St
betrue?
A ∠1三∠2.
B ∠listhecomplementof∠2.
回。lriIa.。ralA。。。isapa.。1°。gram.m
a飾acentanglesarecongruent∵Whichstatement
C ∠listhesupplementof∠2.
mhstbetrue?
D ∠land∠2areIightangles.
A
QuadrilateralABCDisasquare
B
QuadIilateralABCDisarl10mbus.
C
QuadrilateralABCDisarectangle.
D
QuadrilateralABCDisanisosceles
(:S6−1ぼか
trapezoid.
basedonpc重〕manCC(mrCbがed記SLqLIeStions.Copynghl@2009C証romiaDepartmen10rEdue証on.
CALIFORトロ人STANDARDS
日詰豊㌢ateralshoWTnl)el0両atis
ediameter
Ofacircleis12meters,If
po車pisinthesameplaneasth。。i.。。,
andis6metersfl・Omthecenteroftheeire⊥C,
C
i
Whieh bestdescribestheloeationofpoiIltP?
A
PointPlllu買beonthecircle.
B
Po証PilluStbeinsidethecircle.
C
PointPmaybeeitherou扇(尭thecircleor
Onthecircle.
A
D
PointPmavbeeimerinsidethecircleor
On thecircle.
A 53。
(雷のil!
B 1370
C 1800
回
D 233o
回IfABCDisaparalIel。g.am,Whatisth。!.ngth
OfsegmentBD?
A校7C
WhかisIn∠2?
B
C
B ll
D
15。相好 105
A
A 10
C 12
D 14
CSc‥mim
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CllLIFORMA STAND,lRDSTEkT
回ArightcircuIar.。n。llaS.adius5in。h.san。
heightSinehes.
WhatisthelateraIareaofthecone?(Latcrai
areaofeone二でrl,Whereにslantheight)
W′hLtisthea.。a。哩唖r。
l
A 40汀Sqin・
B 445打Sqin.
C 5汀、厨sq証
D S升、暦sqin.
CSGl筋}
“yllndricalbarrelmeasures22inchesin
eterlhowmanyincheswillitrollin
OlutionsaIongasmoothsurface?
121升ln.
1687rin.
1767rin.
ー17 −
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baSedon時論ma博cOnreI眺ed似que諦0博.Copy函1③2009C。l
br…DcpaT山肌0rEdu幽ion.
回
回AsewlngClubismakingaquiItconsisdng
Of25squareswiでheachsideofthesquare
Ofthisfigure、、rillbefbldedup
me謎,uring30ccntimeters・Ifthequnthas
fiveroWSandfivecolumns,iihatisthe
」 5ccntimeters一一一十
perimeteroftllequilt?
A 150cm
B 300cm
C 600clm
D 900clll
CSG〕用ii
回Theminutehandof・aclockis5in.hcsl。ng.
Whatistheareaofthecircle)insquareinches,
i
CreatedasthehandsWeePSanhouI・?
∴∴∴ lVh
atwT i
A lO汀
D
狐‰10肪
C
llbetheと91聖堂.)rthebo
18 −
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CALIFORNIA STANDARDS TEST
i
rectaTlgIeshownbelowhaslength
回Ac・assroomglobehasadiameteroflSinches・
leterSandwidthlOmeters,
4m lz_ 4m
I
l乙
IflbuI’trianglesareremoITedfromthe
ngleassho、Vn,Whatwillbetheareaofthe
Whichofthefbllovnngistheapproximate
Lining庫gure?
Surfaeearea,lnSquZげeinches,Oftheglobe?
A
136mコ
B
144m:
A 113.O
C
168m2
B 226.l
D
184mつ
(SurfaeeArea=祐r2)
C 254.3
C細i;
D lO17.4
GcごくC的
回
IfRSTlVisarhombus,Whatistheareaof
Al XT?
回豊慧諾詩話善書霊警h
radiusof24inches・Sinceroughly75%of
Earth,ssurfaceiscoveredbyW,ateI−hewanted
topaint75%ofhismodelbluetoillustrate
thisfact.ApproximateIyhowmanysquare
inchesonhismodelWillbepaintedblue?
(SumceArea=4詰)
C
D
54 72 鈍 57
B
26 33.40 87
A
A
18誘
B
36、万
C
36
D
48
b妹edonper短m肌Ce。nre厄にed隊団しぼ痛心博ClIPyr回し④2009C同部日日aD叩anm3両()「Edu的くね∩.
回
A 37.5
8 42.5
C 50
D 100
田中atistheam,ins。。ar。in。h。S(in.),。fthe
回航恥r。b。1。、高as。uar。W,ithmr
COngmentparaIlelogramsinside.
C
O
O
D
冶∴∴誘
5 C J
B
2 2 5 .⊃
A
Vhatisthearea,mSquareunits,Oftheshaded
portion?
A 60
B∴84
C l14
D I29
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CALIFORi LASTANDAJtDST
回whatisthearca,insquar。.entimeters,
OfrhombusRSTVifRT=16cmand
回madet、YOCandlesintheshapeofrigllt
angularprisms・The丘rstcandleisI5cm
Sl′=12cm?
l)8cmIong,andScmlVide.Thesecond
dleis5cmhigherbuthastlleSamelength
Width・HoWimuchadditionaIlVaXWaS
ne ユedtomakethetailercandle?
A
320cm〕
B
640cJlll
C
960cm1
D
1280cm〕
R
rSc!Oiie
回申ang}。S。fatria元。ha、,。m。aS。r。S。r55。
A 40
OfthefblloWmgcouldI70tbe
B 48
extehorangleofthetriangIe?
B
0 0 0 0
−ヽJ O −ヽ. 〇
・−・i 2 2 つ﹂
A
C 96
D 192
C
D
回Theperimete.S。ftwr。S。uareSa.。inm。ti。。f
4to9・WmatistheratiobetlVeentheareasof
thetW0Squares?
回
A 2to3
置禁謙語謹書蕊詰
1
B 4to9
Ofpolygonisit?
C I6to27
D 16し08l
CSq:脚il
A
quadri撮eral
B
hexagon
C
L)etagOn
D
deeagon
ー 21−
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basedonpe同町聞CeO旧C厄融tcslquc諦onsCopy直(@2000C【ti
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ABiiの.
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B 60o
O
C
O
D
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D 950
ハ U
A
C 85o
回Ifthcmeasureofan。Xteri。rangl。。fm。guIa.
polygonis1200,hoil7manysidesdoesthe
polygonhave?
A 3
B 4
回
lhemeasuresoftheinteriorangLesofa
摺諾恕藍嵩宝器h。
i
D
5 /O
C
A
B
努tangle?lシ∴∴ j砂∴∴8
28 _四一も㊨TTも新砂
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十ZO 十Zu
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一三竺__i吏__
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回
団Aregularpolygonha叩S鵬・Whafisthe
measureofeachextenorangle?
B
C
D
15 30 45 00
A
回、耽tk,n∠1?
A
B
C
D
A 340
B 56o
回wLatisth。meaSur。。fa。鴎.hra。gl。。ra
regularhexagon?
C 64o
B
C
D
30 00 12 的
A
D 920
ー 23 −
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醇
回A止血Iineisbeingcon里edtore−rOute
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WhichstatementWOuldnotbellSedintheproof
OfthePythagoreantheorem?
A TheZueaOfathangleequals÷ab・
B Thefourrighttrimglesarecongruent・
C TheareaoftheinnersquarelSequal【oh描of
theaI・eaOfthelargeI・Square・
D Theareaofthelargersquareisequa圧Otlle
SumOftheareasofthesmallersquareandthe
氏urcongmentl証ngles・
CSc川iり=
newrouteisestablished?
A
24
B
68
C
92
D
160
ー 24 −
1mPieofCali如ninS伽dardsTb5時C涌onsm諒NOT細Opera血
based伽P諭manceonreie独融te諏qし雌高ons・Copynghl⑫2000&
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CALIFORNIA STANDARDSTEST
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A ananglebisector
B alineparalleltoagl、,enline
C ananglecon rmenttOaglVenangle
D aperpendicularbisectorofasegment
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回FigureABCOisaparallelogram.
LttyPeOftriangJeisfomedbythepoints
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y
hght
equilateral
isosceles
SCalene
CSC川115
回
polnt(−3,2)liesonacirelewhose
tionis五十3)2+(y+l)ユニγ2言Irhi。h。f
Ol10Wmgmustbetheradiusofthecircle?
B
C
D
3 而 9 m
A
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B 14
C14J言
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D
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1 一 4 1 一 2 2 一 打
A ∴ ∴ ∴ ∴ B
ー 35 −
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