2022-2023學(xué)年北京市東城區(qū)廣渠門中學(xué)九年級(jí)（上）期中數(shù)學(xué)試卷

2022-2023(±)

cm2^,^16^)

1.(2#)fêlWb=^iWW.POJJèW^lWJf?^()

A.y=?+3B.y=x2-3C.y=(x+3)2D.y=(x-3)2

2.(2^)M-E^'l'-iL'

()

3.(2#)^^-f-A-é^--7C-^7jf'E?-2A+m=0W--yr^7'J1,WJméW>7()

A.-1B.1C.-3D.3

4.(2#)?fiSIMOrtH-?à(-1,2)()

A.(1,-2)B.(-1,2)C.(-2,1)D.(-1,-2)

5.(2^>)A4X=1,()

A.(X-2)2=2B.(x+2)2=2C.(x-2)2=5D.(x+2)2=5

6.(25>)frlffi,?A,B,C^EQOh,WJZACBftWJ^()

A.60B.30C.40D.20

7.(2#)?AABC^,CA=CB,&o'hABC^gEI'ù',

WA?)CAB()

C.fflWD.

8.(2#)iaMSIftf?

OWiy;?xWPAtt<,tt^M&^y;?M^fn?W

?W^fiM20nWWTOh-Wbixfê,jWJsiè^

J^Wl/^Aiy;??#?W-I$?AJ30TE,?OMIHJ^IAWXTê?BW,?T

(100-x)#,^Wgyx.X4>,?yx(^Wa^

tMSH)()

A.@(3)@B.?(3)@C.?@?D.?@?

A,iMS?#16fr)

9.(2^)M^y=(x-2)2+lCTAêlaWM.

10.(2^)^üèWy=?-2r+H^x$ftl<^,plljk&WMSM.

il.(2^})B￡n.yMx?JI?I^(,Kax>o0t,yBêxKiJ?è't-Méù^iài?

.(^(B-W^M&ù^^apnT)

12.(2^-)(?s,f?AASCAWO!$ta(0°<a<90°)WgljAA/?,B(K1M

JS*DBC±,?IJZADE=.(ffl-a-aaù^T^zK)

13.(2^)A(-2,yi),B(2,yz)?Eüé^y=(x+1)2±,Myiy2

a

yiy2(±?“>”,=”“<”).

14.(2^-)$n?,AD&/ZABCW^f?lSlOOa<JW,^ZBCA=50°,^\ZBAD=

15.(2#)Sllffl,AB%QOMf?,^CDZAB^^H,AB=IO,CD=8,?ljOHift

16.(2$-)toS,?RtAACB^1.ZACB=90°,AB=4,ZBAC=60°,D^JAClM

-^zjbA,BD,CEZBD&E,&AE,WüAE&l?<J<h<

H>(^68^,17-22?,^?5^,23-26?,^?627-28?,<?7^)

17.(55>)?-4x+3=0.

18.(5^)M,△A?Cftf?-TOO,iWAD^j?@|-ù'O.^i?F.:ZB=ZC.

19.(5'T>)TMiOIWSA?SéKj?tg,iMMlfeJit,

BfthM,?>B.cftOOlf?H^a

ZBAC=yZBOC-

1?,2>tW?üt3éKji?ng.

1W?1ktW?20^111^1*)^fê/%3

?0JJ:üE0J3:fc^fèAD.

■:OA=OC,\'OA=OB,\'OA=OB,

.'.Z1=Z2,,'.Z1=Z3.z_____=

éftMWZB(?C=Z1+Z.’?ZBOZ)=Z1+Z3=2Z/

2,1,ZBOD=___________+_

=2Z1,|i?JH!ZC?=2Z=2Z

?’?Zl^-ZBOC-ZBOC—ZBOD+ZCOD|sJSZCOD=2

=2Z_________,Z_________,

WZBAC=-^ZBOC-

2z______=lzZBOC=z_____-

2

z_____

BOC.

=2Z_________-2Z_

=2Z________,

z_____=

A

20.(5#)(-1,0),(3,0),

(i)^gwiwijf?':;

(2)?￥M?4*?xOyltbHtBziMIfcl&fflM;

(3)al<x<40t,MWtByf?MBM.

21.(5ft)#nm,?4X4&ü^f+g-éK43,AABC

(1)M141,

(2)??24>,?SitH-^AABC/jJtWWfi^AASC

(3)??34>,ifflitHAABCggMCfêWfMW

22.(5^-)M,?RtAABC'f,ZACB=90°,ZBAC=30°,

#?E^60O,WSljaUlCD,?&&AD,BD.

(1)f?Jl!!j;i:;i!l'4?l?W;

(2)%BC=\,

23.(6^)B&lATx?ù—7ü—.r+(2-m)x+1-m=0.

(1)M:

(2)m<0,Axi>X2>J@.xi<X2,?=TX2-2XI=3,sjonftùfi.

24.(65>)$n?,?EAABC^,ZC=90°,AD?.ZBACO&ABt~fi,LU

OAfiD,ABTfiE.

ci)W:BC&OO

(2)^BE=2,BD=4,^.QOéWfé.

MWWWêlOat?fi!±l#nTW,?/Kfè/K^?f?^A</*^±fefi,zktt

￡??Wi??WAhA.

d(X)00.7234...

h(^k)2.03.495.25.65.2...

iWW^l?àTl'nl^:

(1)lOE^^WH.fi,

fê;

(2)fetü^^^^^zK^??zkfèKzKYi??^^

X(ffiMO.D;

Z?=-0.3(J-3.5)2+5.675,flhS'a-ffifGW,

M(?“蔓^è”)lOJ/Wh

(4)￡(2)f?W,￡gW??fiWW,BSTSM,l?i?WiJ/KffiM?

^4.2M??,^o^iETOmLSJWM

26.(6fr)ll',*(1,/?),(3,n)MWy=ax2+bx+\(a<0)

±,???x=t

(1)?W;

(2)￡(xo>w)(xo^D^m>/7>l,>ktxoftWilü'êllI.

27.(7?)e^ZMCN=45°,&B?WtgCMh,*ACN(Tpg

*CS-a-).B5&TCNfiD,AB.AD^UCD,F?jfi^BC±,

M?AF=??.AF1AD

(1)^0°<ZBAC<90°frf.

?jRi?E:AF1.AD-,

cD^cAzmn^,?Fig;

(2)^90°<ZBAC<135°H'tCF.CDCA±|0]?Wft^>

28.(7#)flf?P(X/>,yP)^mw,(xe,yQ>’

=XQftf,|y/>-ye|^1,aPWW-4-“?M”.

(1)a$llA(-2,2),B(2,2),?*Pi(-3,3),P2(-1,1),P3(l.4),P4(0,—)

41,J&&&ABtfjWW;

(2)l^WOO.<^y=x+è^x$è.yW?TC>

CDW“?M”,?RbW?f?ffl;

(3)d?n^￡(w,o),l'X#.E^j^-ù'WjE^r^5if??WT&ft:

2

$ù,^-lEW.v±W??^y=lx_2W“M*.”,

2022-2023(±)

-,ifcg???2#,#16#)

i.(2#)rrw?^?wjf?()

A.y=?+3B.y=.?-3C.y=(x+3)2D.y=(x-3)2

[#lf?]?M,Wt?,?HMWr?.

[1?:vy=?inj±?3W,

y=x1+3.

i%^￡:A.

^é.

2.(2#)

[#ffil?EM-;WripSj,

180?,

MA.B,i80Jl?$n

C.

[￡i￥lKé$$

isoSJs-^JIfflSi-ê-.

3.(25?^^Tx6(j—7ü—j^^^gx2-2x+m=0W—>btS^JhWJm?W^J()

A.-1B.1C.-3D.3

[5HJi]O??z^g?X)Ex=Htà-7ü-?^fW1-2+/?=0,MJSJ?

-{fcWBIJnJ.

]W:JCx=lRàTjfêJx2-2x+m=01-2+m—0,

rm/n=i,

BP/nélW?:1.

éfcf?:B.

[?WJ*MlT-7cr^8Ki?:

M-TGZO^W?W.

4.(25?f?Y?S?S?^aWMxOyW3,AA(-1,2)()

A.(1,-2)B.(-1,2)C.(-2,1)D.(-1,-2)

[5X3A^TJM^Waü

[M^lW:vaA(-i,2),

:.A(1,-2),

t&izt:A.

[￡W-J>a?W?WéK?aM

OK^i.

5.(25?fflfid^i-W^i??+4x=l,()

A.(x-2)2=2B.(x+2)2=2C.(x-2)2=5D.(x+2)2=5

[5MJfl

[JimW=?+4x=l,

WJA'2+4X+4=1+4,BP(A+2)2=5,

D.

L&VF1--SS3r?fe,

6.(2^-)ftlg,&A,B,C&?)Ot,AOAB^üH^^,WJZACBèWJ^()

A^~-----B

A.60°B.30’C.40°D.20’

(Mrl^Jffl^üH?^?<lt±^?JWZA(9B=60o,^Js^JffliaiJiJ??SfflWMBP?T

?.

[W^]M:'.?△?AB^iàH?^,

.'.ZAOB=60°,

ZACB=àZA?B=30’,

2

B.

<

7.(2^>)?AABC41.CA^CB,&O$)AB^&.W,-±>C^jHAsCOi<:^J^WOC,

WJOC-tjAB()

(5HIT1JO;oc,OCLAB,fê?gWaWiJ?féWWfê.

[?^]W:?oc,

c

\‘CA=CB,￡OAB+,i>,

0C1AB,

VyAcCO

cJiJAB?WM^TOCa<j4M￡.

.-.ocAiAB?,

C.

^AWIgfiWiL

8.(2fr)x,üéMBIftéltj

?W3y;?xWPAtfcW,W^I'HJWJ—iatbW.btWlWAAAiy:(D^M

?éEé?^M20/,itJciJ^JsM^in^S,attiraxfê,

^ft^S^y;?WiWnWJW?Ai30je,?WlW?bAWxjcHJ#,nT

(100-x)ft,WJAjyic.M+,$*yA?$*x:tlWM?(Wf§B$

WMS)BlWffl-^7Fn[R]±a<JiiéW^^M()

A.?@?B.?@?C.???D.?(2)(3)

J?J

[^HlflWISl,W^Hl#M\?4y-!gxAiWmW-g-4?

Wffn^TnJ,OJBTM^M.

tamw=Eti^sniw,

~?l?lttWii3j^’?;‘JfSffi￥-?x,^IWifKj^cWn^y,WJy=2Trx,x+2nx2=2nx2+2nx2

=4TTX2,i￡ê§a^Fafà±lWI^5,

X??$PàLtW,^KPAZl'aJiif?-^ttW,y,WJy=àr(x-1)=àx2-lx,

'222

ifliiJ^JHiWWJJU^fi,to^W^tt±-WJ)Uxf?,R

^Jsiè^p'àW^M^y,WJy=20x-x=20?,i^MAlJFnfà±?W?,

.1:

￡MBWJW?AJ30JC,?M^I'nJAJ^WWxjclLlW,WH1(100-x)#,

m’^yjü,WJy=(x-30)(100-x)=-x2+130x-3000,iOJ&^nfàTWJO

feijfc:D.

?S?5^16#)

9.(2#)Htà^y=(x-2)2+lf?WM(2,1)■

[WJ

TOW:SMy=(x-2)2+l??M^^^,

<2,i).

[-?àVFlaCx-h)2+k,Tü???SM(k,k),M^rtlz^jOJsx=h,

T^M?fflt^.

10.(2#)y=x2-2x+kxWJkMWi??WJSk^l.

[frtJrlWT^BPWHlkMMMH.

[?:vJJè?y-x2-2x+kWX

;.A=(-2)2-4XlXk>0,

Wlrhk^l.

k^l.

[￡i￥lxttaWa.éM?y^x2

-2x+kX$fhW3c^W5ijA>0,Wrli^Tk

11.(25>)K^x>0Ht,yfax?W^M'J'.

?TMy=l(x>0),g?feW-■

x

[^tffiaMyPJaüMx^^^m^,wj&tn

Rgk<0,WJRtt#?a3H-ai!grt,8?yPI

ê?x^^?fi?±^.

[ftmM:HMffiRt^JMIfc^ogpnr.￡ny=l(x>0),

X

y=l(x>0),^W~.

X

[￡i￥]y=A(k^o>MM:?k>oet,

X

-,=w.a<?apgrty^xM±t*?fi?M^:?k<ont,raw.r±

^'hWl*!yHxSW^?W^.

12.(2^)M,WAAfiCgg?4Jlf?BHI-j^a(0°<a<90°)fOJA?Dê,,?M?MM

SaDfè^?üBC±,WJZADE=90°-1Q.(ffl^aM^T^)

------------2

m/r1AI)=AB,ZADE=ZB,

=ZB,%.'fêZADE=ZADB=90°--1Q.

2

[W^lW=AD=AB,ZADE=ZB,

:.ZADB=ZB,

VZBAD=a,

:.ZADE^ZADB=1.(I20O-a)=90°-—a>

90°-la.

2

13.(25?A(-2,yi),B(2,yz)OWSy=(x+1)2±,Jü!|yiyi

VI<V2CW“>”,“=”SK“<”).

[5HJrJn,

2

[A?^]W:’.'&A(-2,yi),B(2,y2)(x+1)Jt,

.*.yi=(-2+1)2=1,(2+1)2=9,

.*.yi<y2,

<?

14.(25>)^nS,AD^AAfiCf?fl'fêiaiOO%ZBCA=50°,W1ZBAD=40°

[W1

W:"AD%&ABCfàW&?G)Ofà?.&,

.’.&A,B,C,D&?)O±.,

VZBCA=50°,

.'.ZADB—ZBCA=50°,

‘:AD&&ABCaW^ElOOWM,

.’.ZABD=90°,

.’.ZBAD=90°-50°=40”,

40°.

r/un@m?s,ém??sms!izAr>B=

50°,ZABD=90°MMW^.

15.(25?AS^JOOWM,&CD.LABH,%AB=10,CD=8,MOWW

3.

[5HJrlCDl?BW?lJCH=±CD=4,WfOSWféWMHiOH=3.

2

[?￡]W:'^OC,

'.'CDZAB,

:.CH=DH=^CD=Xx8=4,

VM^?B=10,

:.oc=s,

&RtkOCH^,O^=7oc2-CH2=3’

^^^9:3.

16.(2#)M,léERlAACB^,ZACB=90°,AB=4,ZBAC=(AF,D&üAC±.ff'J

&&BD,ftCE.LBDTtiE,T&&AE,K'JAEW'httft_'j7—/3_-

IftWlW-BC^tiF,&&AE,EF.B#a￡?WfiC^Mfea<j|g|^±±J?^,S

&A,E.?E<m.mi+irw.

??:?SCW.F-'&&AE,EF.

A

’.'CEZBD,ZBEC=90°,

:.BCK^lWJlSI^±is^j.à^A,E.F?|s]-M±rt,AEM.

?RtAACB^.ZACB=90°,AB=4,ZBAC=60°,

:.BC=AB’sinZBAC=4X^2-=2\/3’AC=AB‘co$ZBAC=4xl=2,

22

ZBF=FC=EF=1BC=-/3>

2

’*??F=V22+(V3)2='FI’

:.AE=AF-EF=yJ7~yj3,

BPA￡?ü?/ba^V7-V3-

V?-V3.

[MOJIlAlWm'?W^Wù'iê

>5H(fi￡??ij?Jijg(fiaê?Jx￡WM(fi￡.

H,f?&g(&68#,17-22?,<?5#,23-26?,^?6^,27-28?,<?7#)

17.(5fr)x2-4x+3=0.

[WrlOE?Wt?m

W:?-4x+3=0

(x-1)(x-3)=0

x-1—0,x-3=0

X|=l,X2=3.

18.(5?)M,△ABCrtféTOO,^UDOI^ù'O.j^iiE:Z.B=AC.

iWWW^fè.

iJEHJJ:VAD1BC,^ADM-ùO,

'?AB=AC,

:.AB=AC,

:.ZB=ZC.

[Ai5?]iJêB?iI,m

19.(5Z7>)

01^^?S:-OlJWWHOMl?*èWil'ù'?-*,

W:nTU?^H^.

Bftl:M,4,B.

ZBAC=yZB0C-

1MM,5^1#?2>W3(W

1tWJ5A2HbC?IHI^?iAiaBtt?l3

?:ilEBJ-]:Mfé/W.im

\'OA=OC,\'OA=OB,‘:OA=OB,

/.Z1=Z2,.'.Z1=Z3.:.zOAB=z

è^AnJ-fl,ZBOC=Z1+Z2,?'.ZBO￡)=Zl+Z3=2OBA.

ZBOC=2Z1,Zl,:.ZBOD=ZOAB+

?’?Zl=yZBOC-|s|?SZC0D=2Z2,ZOBA=2ZOAB,

.?.ZBOC=ZBOD+Z|sjBfiZCOD=2Z_

BBZBAC=yZBOC-

C0D=2ZBAC,DAC,

:.ZBAC=àZ:.ZBOC=ZCOD-

2

ZBOD

BOC.

=2ZDAC-2Z

04B

=2ZBAC,

:.zBAC=-^ZB0C-

A

(#W1*|JWWBPnf.

[iiF.ng:1WS1,￡o&ZBACaü-ü±Ht,

\'OA=OC,

:.z\=Z2,

é^?f?JW,ZBOC=Z1+Z2,

ZB0C=2Z\,

:.Z\=LZBOC,

2

BPZBAC=-lz50C,

2

ZBOC-,

tW??2,^èL^AD,

’:OA=OB,

:.z\=Z3.

:.ZBOD=Z1+Z3=2Z1,

RSZC?D=2Z2,

ZBOC=ZBOD+ZCOD=2ZBAC,

ZBAC=1ZBOC,

2

2;BAC-,BAC-,

WZ513,imiAD,

\’OA=OB,

:.ZOAB=ZOBA,

ZBOD=ZOAB+Z0BA=2Z0AB,

^■.ZC0D=2ZDAC,

ZBOC=ZCOD-ZBOD

=2ZDAC-2ZOAB=2ZBAC,

...￡Z,101-...X

:W(J)

?￡+^v

‘i-=?[|a-fi?ü*t??

‘?tz-

:

z(I-X)v^Di-xvz-j?=(￡-x)(I+X)P=.<￥WWWW&(I)W[W]

??ww?(D

^fiaww<2)

”?P￥￡￥WWié‘(￡-n(l+x)(D

?fflWW^FRê;?‘WS^S-^-Ww>r>l￡(￡)

‘WTOW^-fPffl%Ao-viMWWfflzt#(2)

(I)

?tzCT^WK‘(0“￡)‘(0‘1-)(^?)'01

www?Swè^IMIXWWt*ii

■jva

■3vn‘a(chǎn)vo-Dva-aoa-CIOD‘-DVCI-avo‘-vaoz-avov-vao-avo

??097y=jy37v

y...03430...

(3)Vx=10t,y=4,x=4ltf,y=-5,

.'.èffltW=ll<x<4ll't.y^?ffli-5<y<4.

[SI,W&WW?fêMé?.

21.(5^)?nISI,&4X4ftWW-l1,/\ABC

(1)M1+,

(2)?S2+.iSldi—^△ABCJ^tt^M-^AABCW^üWaH?^;

(3)?￡|I|3^,iHlHJAABC^#,^COlltm^fàO^O0

[5H/f](1)^-4>'ù^6ù^BPWH1S^;

(2)f??XOW±?W!±{TO;

(3)

[ftmiW:(i)

(3)ftW/fzr;

E__A

B

§13

△CCD

22.(55>)M,?êERtAABC41,ZACB=90°,ZBAC=30°,MgtCAC

#^60°,CD,JèfêAD,BD.

(1)

(2)^BC=\,?^&BDtfrtz.

(2)^O30/OM?HO^UmWtt^?OMD=AC=V3?ZDAB=90°,M

[)???]?:(1)fcffl,

(2)?RtAABC4?,ZACB=90°,

'.'ZBAC=30°,BC—l,

C.AB=2BC=2,

:.AC=^3,

èWnlfrl:ZDAC=60°,AD=AC='[?,

:.ZDAB=ZDAC+ZZAC=90°,

?’?BD~VAB2+AD2-V22+(V3)2-^7?

[^i￥lW?S,W

23.(6^)xéKj—-JCZJ^+(2-/??)x+1-m=0.

(1)4<üE:

(2)m<0,xi,X2,Jlxi<X2>^X2~2xi=3,in[l'jffii.

[^HFf](1)?i+WWWSlJ^OjA=m2>0,

(2)xi=m-1,X2=-1,MWUX2~2xi=3-1-2Cm-1)

=3,^JHW^W^WBP??T.

[(1)i?F.R|:VA=(2-m)2-4(1-m)

=w2^0,

(2)ft?:x=~±m(xù).

m<0,x\<X2>

‘.x\—m-1,X2—-1>

’.'x2~2xi=3,

/.-1-2(m-1)=3,

m=-1,

B|Jm-1■

[?WJ-TCZl^Wax2+bx+c=0(a^O)A=b~-4ac

^A>OHd-,^A=Oitf,

aA<ont,

24.(6^/>)M,?A?fiC41.ZC=90°,O%ABt“jS,

OAD,5gABAr^E.

(1)j￡?:BC^OOim?

(2)^BE=2,BD=4,^Q?a<j￥-B-

[W1(Dt?10W￡W?5(.fOlJZBAD=ACAD,tOWH?^WtWW?iJZ

BAD=AODA,?i?i?fa$jAODA=ACAD,MOD//AC,fOüODABC,

(2)

(Wg]d)?O:AAD&ABACtfrfft?,,

ZBAD=ZCAD,

■:OA=OD,

ZBAD=ZODA,

ZODA—ZCAD,

OD//AC,

’.'zc=90°,

J.ODZBC,

VOD&Q0iW,

:.BCWom;

(2)W:

?RtAO&D't1,OB2=34OD2+BD2,BP(r+2)2=r+42,

WW:r—3,

.?.OO?<JW^93.

25.(6i?)OMlUIiSIM--?zJctm-T

???zKfèzKY?M^dMM,zKtt

hx.

d(X)00.7234...

//(X)2.03.495.25.65.2...

(1)

fê;

(24Hffla,f?tH^M?üB7K*?zktaa<J7m?M^6.7X

(ffiiOlJO.l);

(3)(2)6ù>frT,’W/^^zK?WiJ^f?zK'/èrtjà^,

M^tB?ù7KO^Bü?a>9/2--O.3(J-3.5)2+5.675,W?

7%(?“è”Wc“^è”)^SljTk'/lk^;

(4)?(2)ü^lHTM4X,rjWJzloSM?

WW&OJéW&.

(2)JE/7=ORàBP?T;

WWtBépfè;

(4)JEd=5RA—hWffi,H-tg4.2LUWnj.

'&h=a(J-3)2+5.6,

JE(0,2)RàBJW?=-0.4,

:.h=-0.4(J-3)2+5.6,

^/z=01ft,-0.4(</-3)2+5.6=0,

(/=3+V14?t3-V?4().

3+V,r?4^6.7(TK),

&6.7%,

6.7:

(3)V-0.3>-0.4,

(4)at/=3+A=5B|,/z=4<4.2,

2

g;MO??fê.

26.(64?)??^FiS??xOyrl’,&(1,m),(3,n)y=ax2+bx+l(a<0)

±,????!;*)x=t.

(1)a/n=?ff'f,

(2)(xo,m)(xo^l)?ito^l^S-h,?rm>n>\,>KtxoffùIXiê'/èBI.

(1)(1,m),(3,n)Rà?è^afê^tlf^,m=nf#tljb—-4a,S

WWWRT;

(2)S^m>n>l,W?tB^WéKjWrè?,MW?xoWW?êH.

[W^JIW:(1)Vax=OHt,y=l,

/.Wté^y$|113￡*éKJ^^(0,1),

*/,iü(1,m),(3,n)y=?x2+èx+l(a<0)J2,m—n,

,'.a+b+\=9a+3b+?,

’.b=-4a,

--L=-Z4a=2.

2a2a

:.t=2-,

(2)’.’m>n>\,

:.a+b+\>9a+3b+\>\,

WW-3a<b<-4a,

:.4a<-b<3a,

?3a-b<4a

2a2a2a

g|]?<r<2,

2

xo=2;

2

a/=2Ht,à'O=3.

/.xoMWMffl2<xo<3.

(aifl

27.(7^-)&?ZMCN=45°,?CM±,￡ACN±fl<J—(^

?Cfia).OàRADfflCD,&FBC±,

K?^?AF=AB.AFZAD^I&AL.

(1)Ml,^0°<ZBAC<90°Ht.

?>KüE;AFZAD-,

?^W^CF,CDCAZIWJW^,?01;

(2)a90°<ZBAC<135°fit,CRCDCAZl’a]

&CD-CF=-J?AC.

(1)?MWtfWft^W?lJAABC^AADC,$C?4ZABC=ZADC,ZACB

=ZACD=45°,

?i±A^APZAC^CBP,àfcf?AAPCZPAC=90°,

AP=AC,mZPAF=ZDAC,W

?üé?i-ê;

(3)M2,üA^APZAC^.CB^^7^-P,tt^AAPCZ

PAC=90°,AP=AC,'^\ZPAF=ZDAC,WM?=W

W:(I)

.’.A?BC^AADC,

.’.ZABC=ZADC,ZACB=ZACD=45°,

:.ZBCD=90°,

\’AF=AB,

:.ZABC=ZAFB,

ZAFB=ZADC,

VZAFB+ZAFC=\W°,

ZADC+ZAFC=180°,

ZFAD=360°-(ZAFC+ZD+ZFCD)=90°,

.’.AFZAD-,

AAPZACCBTF,

.’.A?PC^WSAH^^,ZPAC=90°,AP=AC,

?:ZPAF+ZFAC=ZDAC+ZFAC=90°,

ZZPAF=ZDAC,

VZAFB=ZADC,

ZZAPF^ZACDCASA),

:.PF=CD,

PF+CF=PC=\[2AC,

:.CD+CF=y[2^C;

(3)^90°<ZBAC<\35°fcj-,^Ll[?|2,

üAAPIACXCBP,

ZZAPCZPAC=90°,AP=AC,

VZPAF-ZFAC=ZDAC-ZFAC=90°,

ZPAF=ZDAC,

VZAFB=ZADC,

ZZAPF^ZACDCASA),

:.PF=CD,

+,PF-CF=PC=4?.AC,

'.CD-CF=y[2AC,

CD-CF=J?AC.

fiüiOL

28.(75)-)XtT-^PCxp,yp)^J&W,W±#?“^QCXQ,yQ\iéWaxp

=XQW,|yp-yG|^1,PW?<J-^“?M”.

1

4.“?J2*”fl<J^P2,P4;

(2)1>J￥^OO>y$fhOJ￡Tc,￡>j#i^,

?CDlfft-OlOOW“üM”,

(3)BME(?n0),LU*E^+?W?EWs^?yT^#:K^iiSm?^S

2

?J,Mi<:^l.?jE^y±OT?y=|x-2&ü“M*”,W^LB/n^M

iuHI.

‘l

*woroajw.-

<DW.cv

■*d^d

‘??'OT