2023届辽宁省大连九年级数学第一学期期末质量跟踪监视模拟试题含解析

《2023届辽宁省大连九年级数学第一学期期末质量跟踪监视模拟试题含解析》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2022-2023
ᦪᔁὃ1.ᐰᔁᑖ⌱⚪⌱⚪ᑖᐰᙠ⚪஺⌱⚪ᵨ2B!"#$%⌱⚪Ḅᫀᵨ(⁐*+Ḅ,"ᡈ*"ᑏᙠ“⚪”1234஺2.5ᵨ(⁐*+Ḅ,"ᡈ*"ᙠ“⚪”ᐜ#ᑏ789ὃ:;஺3.<ᢝᓱ☢@AB⌕ᢚEB⌕FẚஹFIᙠ₝Kஹ⚪ᔁ⚪Lᦔ஺Nஹ⌱⚪OPQ⚪3ᑖᐳ30ᑖS1.TᐵVxḄWXYᦪZ=ᓄ—1/+2%N3
1+%+2Ḅ^_ᙠ`abcdᐵV”Ḅᑖebf9km-4-1_IQ----------+2=NWᨵ᦮ᦪiᑣklmnoᩩqḄ᦮ᦪroᦪᨵ
.m-33-mA.2oB.3oC.4oD.5o2.᝞^PA.u8vw஺஺Ḅᑗyᑗzᑖ{|AஹB.}~AC8OᑁV஺஺஺uᑣᑡ┯ḄwB.ZAPB+2ZACB=180°C.OPABD.ZADB=2ZAPB3.ᑡeywxḄYᦪḄw
x1c2A.y=-B.y=--C.xy^-2D.y=3x+3x4.᝞^A8|Ḅ஺஺ᨵNzC,dN5OC=50஺ᑣNAḄᦪ|O)A.65°B.50°C.30°D.25°5.NḄᱏᢚ1ᜧQḄ1wO
A.V2B.4:1C.3:1D.2:16.Tᙊᑁ¡Ḅ☢¢|3£ᑣ~¤¥wOS/7A.2B.1C.73D.—2

17.ᙠ¦☢¡ᙶ᪗©,zA(0,2)ஹB3/+2)ஹC(ft,O)(a>0,/»()),«AB=4¬dNACBᨬᜧlbḄr|()A.2+2°B.-2+276C.2+4&D,-2+
8.᝞^ᙠbABCDzEwCDḄzzFwBCḄNzdBF=3CF,AEஹAF,EF,ᑡজNDAE=30஺©AADE^AECF,ঞAEJ_EF,@AE2=AD»AF,ᐸ²Ḅoᦪw()C.3oD.4o9.᝞^R/AABC´zA⌮l┐·¸50°¹ᑮRt^ABC',zCា¼½ᙠ~ABḄzCᜐ,BB'ᑣNBB'AḄᦪ|()A.50°B.55°C.60°D.65°10.ᐵVxḄNᐗWXbfx2+ax-1=0Ḅ᪷ḄÁÂw()A.ÃᨵÄᦪ᪷B.ÅᨵNoÄᦪ᪷C.ᨵo1ÆḄÄᦪ᪷D.ᨵoB1ÆḄÄᦪ᪷Wஹ#Ç⚪(PQ⚪3ᑖᐳ24ᑖ)11.᝞^}~ABCDwÈND48=50°¡yAC,8஺1ÉVz஺DHABH,OH,ᑣZDHO=_________.12.᝞^oᜧQBkḄ¡ËÌᙠkN¦☢ᑁ¡⚔zÎᔠVzC,z஺ᙠA3N84C=N£>EC=3O°,

2AC஺ÐÉVzuAE,BD=1,AD=5,ᑣ"=13.᝞^0஺Ḅ8Ó|6,zEwCONzdCE=1,ÔzEÕᑣÕABÓ|14.Ö3,1,-2×oᦪØÙoBkḄᦪ|PzḄᙶ᪗ᑣPzÚ¼½ᙠÛ}_▲Ḅᭆ᳛wN.15.ßàáâãäᨴæ├è400éêᨴæஹëᨴæ├èìíîÓëᨴæ├èìïᑮ576éᑣðàáâã×oᨴ├èìḄᨴ¦ᙳîÓ᳛|.16.ᐵVxḄNᐗWXbf3(x-1)=x(1-x)Ḅiw.17.᝞^òA3CD´z8ól┐·¸90஺¹8£FG,«43=3,BC=2,ᑣ^▢õᑖḄ☢¢|18.᝞^öᱥyi᪆e|y=f,z4Ḅᙶ᪗|(1,1),04Ô44ᡠ஺Qᑖ{ÉyaஹöᱥyVzuúBi;ÔBi8mᑖ{ÉyaஹöᱥyVzP2ஹAz;ÔA2û||4%ᑖ{ÉyaஹöᱥyVzu3ஹü…%ᑣzḄᙶ᪗w.

3yBஹDE⚪(ᐳ66ᑖ)19.(10ᑖ)᝞'%0AஹBஹCᙠ஺OI%ᵨKLMḄNOP'.(1)ᙠ'জR%PST4NBU⊡ḄᙊᕜY(2)ᙠ'ঝR%PST4NBU[ḄᙊᕜY.00'জ'ঝ20.(6ᑖ)᝞'%=/஺%\ADN]^0஺%-AC/0£ាᨵCE=AD,()OE.(_1)᝞'1,`abACDEABD'1(2)᝞'2,()*ᑖ,-A஺%஺஺/0£G,()AGOG123OG48ᨴ67Ḅᦪ:ᐵ<%=>?ᳮᵫ;

4(3)ᙠ(2)ḄþẠ
DG=4iADḄ.21.(6ᑖ)᝞
ᙠAABC
AB=AC,A0Ḅ
E.(1)ABDE^ACAD(2)43=13,BC=10,£>EḄ.22.(8ᑖ)᝞ᩩᑖᡂ3!Ὺ
ᡃ$%&ᩩ'(&Ḅᑖ.᝞1,%)⚔36஺Ḅ!Ὺ,ᱏ.ᑐ
ᑖᡂ3)0,ᱏ
12)0,ᱏ34!Ὺ
ᡃ$%&ᩩ'(!ῪḄᑖ.1(1)᝞2,5ᵨ789Ḅ:;<=⚔45஺Ḅ!ῪḄᑖ
>᪗@2!Ὺ⚔ḄAᦪ:(7:;ᑖEḄᡂ3Fᐰ!
ᑣI97).(2)᝞3,AABC
AC=2,BC=3,ZC=2ZB,5<=AABCḄᑖ
>=ᑖḄ.23.(8ᑖ)8JKḄLMᨵOPᐰQ9Ḅ0ᳫ
%S$ᑖT᪗U1,2,3,4.VW᥎Y0ᳫᯠ[\]
^VW᥎=0ᳫ
5ᵨ᪛`ᡈᑡ⊤;dᑡefḄᭆ᳛.(1)iY=Ḅ0ᳫḄ᪗UQ9j(2)iY=Ḅ0ᳫ᪗UḄk!6.

524.8ᑖmᙠnABC஺
AB=6,4£>=8,E4AQ
EMLECoAB/
NᙠqMB
rAE44MkANḄst⚗.1
᝞1,ZANE=NDCE2
᝞2,vNᙠMBwx
ὶzAC,rAC{NE|Qᚖ~
MNḄj3
ὶzAC,᝞A/{EஹMஹN⚔ᡠᡂḄQ
஺EḄ.25.10ᑖmᕜᜧ᱅ḄᲦ᪻ᜧḄ᰿
Ღ᪻ᡂ[
10ᜩḄ├ᦪk├ᓫ¢
ᐸ├ᓫ¢y¤ᐗ/ᓟ§m{¨x©xᜩx᦮ᦪmḄᦪᐵ¬᝞ᡠ
®├P¤ᓟ§m{¨x©xᜩx᦮ᦪmḄ¯ᑖF°±᝞⊤ᡠ:e7fXᜩ135710h├j:Pᓟ220260300340400l
1
5~²ᑏ=p{xḄ´ᦪᐵ¬µ¶·¸xḄY±º;2
y{xḄ´ᦪᐵ¬µ
>ᑏ=·¸xḄY±ºj3
ᙠ&10ᜩ
¼ᜩ├½¾ᑮᨬᜧ
ᨬᜧ├½4ÁÂᐗ.26.10ᑖm᝞
ÃÄOABCDᑁ²ᙊ
FAC{BDQoE,FᙠAC,AB=AD,ZBFC=ZBAD=2ZDFC.

6B1NDFC=40஺
NCBFḄAᦪ.2CD±DF.ÈὃÊᫀஹ⌱Í⚪¤20⚪3ᑖ
ᐳ30ᑖm1,BூÑ᪆௃ᐵxḄÔi´ᦪ>=
Ö-ld+2"3
x+Ö+2ḄØᙠxÙ:
Ú=ÖḄº
᪷Üᑖµ:Ý᦮ᦪÑ
Ú=஽Ḅ±
ᓽàÑ.ூáÑ௃ᐵxḄÔi´ᦪy=
%-lf+
2Z—3x+Z+2ḄØᙠxÙ:
âij1-1>0—.16ᑖµ:ÝãᑖäE2å;+1+2æ-3=19,»12ÑEm=-~᝕+1vᦇ=2¨
æ=4vÖ=3¨
æ=3¤êãmjvᦇ=5¨
m=2vᦇ=11¨
m=l9¨ëìᩩfḄ᦮ᦪk±ᦪᨵ3.ᦑ⌱:B.

7ூî௃ὃïᑖµ:ÝḄÑ
Ôi´ᦪḄØ{ឋñ
òóôᑖµ:ݶÔi´ᦪḄឋñ4Ñ⚪Ḅᐵõ.2ஹDூᑖ᪆௃ö²04,0B,᪷ÜRUP834஺஺Ḅᑗ
ᑗᑖTAஹB,ᑮPA=PB,0PAB,ᡠA,CøÚj᪷ÜN0AP=NOBP=90°Eᑮ=180ᓽ44ù8+2N4C8=180°,ᡠBøÚjÜúàEÊᫀ.ூáÑ௃Ñ᝞
ö²஺4,OB,•■PA.PB4஺஺Ḅᑗ
:.PA=PBOP1AB,ᡠA,CøÚjû,.,Q4LR4,OBLPB,NCMP=NOBP=90°...ᙠOAPBO
N4PB+2403=180°,ᓽNAPB+2NACB=180°,ᡠBøÚjYDüý
þ;KNA£>8=2NAPB,ᦑD8øÚjᦑ⌱D.ூî௃ÿ⚪ὃᙊᙊᕜᙊḄᑗḄឋᑗᳮ៉ᐵឋ⚪Ḅᐵ.3ஹCூᑖ᪆௃᪷!"#$ᦪḄ&!"#$ᦪḄ'()y=&(kWO),ᓽ+ᑨᔜ$ᦪḄ./ᔲ1ᔠ⚪3.XYூ4௃Aஹ5=89"#$ᦪ┯;='2!"#$ᦪ9?

8p⚪ὃrstuvᦪḄwxᱯ0%stuvᦪD᪆{ḄS|}{~by=8(kWO).X4ஹDூᑖ᪆௃᪷ᙊᕜYwᳮᓽ.ூD௃DbᵫᙊᕜYwᳮ%ZA=1ZBOC=25°,ᦑ⌱bD.ூ0௃p⚪ὃrḄᙊᕜYwᳮ%ᙠᙊᡈᙊR%ᡈᡠḄᙊᕜY%/ᩩᡠḄᙊYḄS.5ஹArs1ூᑖ᪆௃}Ḅ~2a,~b,ᢚᡠḄ}4}%ᑣ¢=2balab}Ḅ~2a,~b,ᑣᢚḄ}Ḅ~b,~a,••,ᢚᡠḄ}4}%.2ab••---=-9ba...ᜧ}4¥}Ḅt0:1;ᦑ⌱A.ூ0௃ᳮD¦b᝞§¨T©ᦪḄª©}Ḅ«Y%«©ᡂtu%¨TᡈªTª©}®ª©}%ª©}«©Ḅt®t.6ஹBூᑖ᪆௃᪷⚪¯P°'}%()AO=±-8c/0%ᑣᵫBY}²Ḅឋ´AZ)=3x,ᑭᵨ┦YBYvᦪ⊤¸°BOḄ%ᵫᚖ]wᳮ⊤¸°5cḄ%ᯠ᪷☢¼½DEᓽ.ூD௃᝞'%

9()4஺=±-8c/0O,¾IJ4O_L8C,OO=x,¾¿jAO=3x,BD'
tanZBAD=——AD:.BD=tan30°,AD=Àx,:.BC=2BD=26x,v|fiCA£)=3V3,ÁX26XX3X=3G»,.x=lᡠ\ÂᙊḄᑁ)ÄB©}Ḅ©Å~1,ᦑ⌱B.ூ0௃p⚪ὃrĪ©}Æᙊ%BY}²Ḅឋ´%ᚖ]wᳮ%┦YBYvᦪ%☢¼½`ÇÈḄ%DEp⚪ḄᐵÉ?Ê⚪¯%`°«Ḅ'}Ḅ©Å.7ஹBூᑖ᪆௃᪷ᙊᕜYᜧ/«Ḅᙊ᜜YÌAABCḄ᜜)ᙊ4xÍᑗe%Z4C8ᨵᨬᜧÐ%ÑeᙊFḄÒᙶ᪗4C0ḄÒᙶ᪗%=ÕᙠÖ×ABR0Õ4NÇABᚖNḄNÇI%᪷FB=FCᑡ°ᐵ/bḄÙÚ`Dᓽ.ூD௃DbAB=4&
A(0,2)ஹB(a,a+2)AJ/+(a+2—2)2=472
D஺=4ᡈ஻=4(Ü~஺Ý0,Þß)B(4,6),NÇABḄD᪆{~y=kx+29àB(4,6)áᐭk=l,ᡠ\y=x+2,ᑭᵨᙊᕜYᜧ/«Ḅᙊ᜜YÌAA5cḄ᜜)ᙊ4ãÍᑗe%ZAC2?ᨵᨬᜧÐ.᝞ä'%G~ABR0%G(2,4),

10y×0GÕᚖN/ABḄNÇl-.y=-x+m,àG2,4áᐭ/஻=6,ᡠ\y=-x+6.ᙊæ"S"6,ᵫèC=EB,é7+62=•S42+—"6—62,Dê=2#S2ëÞßìÐ
.ᦑ⌱bB.ூ0௃p⚪ὃrᙊḄíᔠ⚪%SïvᦪḄ«ᵨÆëé¨0ᙶ᪗%ᵨðñwᳮ`¨0Åò.óôᔠᙊḄᑗÇÆᙊᕜYwᳮ᪀ö'}÷ᑮC0ḄùúDûÑ⚪ḄᐵÉ.8ஹCூᑖ᪆௃᪷⚪¯tanNZMEḄÐ%üýᑨÿজ
Ḅ4a,᪷⚪ᵨa⊤FC,BF,CE,DE,ᯠ᪷Ḅᑨᓽঝᑨ!
ᙠঝḄ#Ạ%ᑭᵨḄឋ(ᓽ)ND4E=NFEC,*+ᑭᵨḄឋ(ᓽ)ᑮNOEA+NPEC=90°,-ᑨ!ঞ
ᑭᵨḄឋ(ᓽᑨ!ট.ூ23௃35•7A3஺9:EQ9;<:.•.CE=E஻=[OC=!AO,22DE1.tanZDAE=—=-,.,.NZMEW30°,ᦑজ┯?
AD2Ḅ4a,ᑣAC=a,BF=3a,CE=DE=2a,DEADDEAD,-----=2,------=2,♦.------=------,CNZJ=NC=90oFCECFCECt:.XADESXECF,ᦑঝD;VAADEsAECF,:.ZDAE=NFEC,

11VZDA£+ZD£A=90°:.NDEA+NFEC=9Q°,
.AEYEF.ᦑঞD
A£)AEVAADE^AECF,——=——
.AE2=AD*AF,ᦑটD.AEAFG%:DḄHᦪᨵ3H:ᦑ⌱5C.ூ0,...qᨵrHsUḄtᦪ᪷.ᦑ⌱D.uஹvw⚪xyz⚪3ᑖ:ᐳ24ᑖ|11ஹ25ூ3᪆௃✌ᐜNHDBḄᦪ:ᑭᵨ;ᳮ)OH=OD,ᵫ)NOHD=NODHᓽ3⚪.

12•EFGABC஺IG.ACLBD^O=OB,ZDAO=ZBA0=25°,AZABO=90°-ZBAO=65°,•
DHLAB,".ZDHB=90°,AZBDH=90°-ABO=25°,ᙠ&ADH3LOD=OB,.OH=OD=OBf:NDH(ANHDB=25°,ᦑMᫀOB25.ூCD௃P⚪ὃIGḄឋQRGSFLᳮTUVឋᳮ⚪Ḅᐵ.12ஹ#.3ூ᪆௃WCCXCMJ_DEYCM,WCEXEN_LACYCN,ᐜ[BCDs^ACE,\]AEḄ^NCAE=60஺_]NDAE=90°,ᙠR£DAELᑭᵨbcᳮ\]DEḄd'e\]CDḄᑖfᙠRSDCMR3AENL\]MCNEḄg[MFCs^NFE,ᑭᵨhRGijFḄ"kᓽ+\]CFlEFḄ"m.ூ4௃B᝞oWCCXpYCWC£XẬ4cYCN,,:BD=1,AD=5,AB=BD+AD—6•.•ᙠRfAABCLZ5AC=30°,N8=90°—NBAC=60°,

13BC=LAB=3,AC=6BC=362ᙠRt\BCAlRt\DCELVNBAC=NDEC=3(f:.tanABAC=tanZDEC,.BCDC••—fACECVNBCA=NDCE=96,,/BCA-ZDCA=ZDCE-NDCA,:.NBCD=ZACE,AAfiCD^AACE,.஺.BCBD♦•NC4£=NB=60:.ACAE31rZDAE=ZDAC+ZCAE=300+60,=90°,—f==—3V3AE•••AE=BᙠR/A4OELDE=^ADr+AE2=752+(73)2=2:ᙠRfADCELZDEC=30:•NEDC=60DC=-DE=sf7,2ᙠ&ADCMLV3_V21MC=—DC=-----,22ᙠRrAAENL᧗.3NE=—AE=—,22VZMFC=NNFE,NFMC=NFNE=90஺.\MFC^/SNFE,V21.CF_MC_V21,•NEt'u'2

14ᦑᫀ5.3ூ

15wx•.•ᐳᨵ6·UḄ®:ᐸ;(1,-2),(3,-2)<±ᙠ²7³▲:21...P<¯°±ᙠ²7³▲Ḅᭆ᳛:=:,63ᦑᫀ53ூ

16917ஹ—714xᑖ᪆1BD,BF,᪷SK»=SAABD+SᓭzBDF+SABEF-S{GABCD-S#GBCEᓽ)ᫀ.ூ23௃᝞¬:BD,BF,ᙠçABCD;:NA=90஺:AB=3,AD=BC=2,•••BD=VAB2+AD2=V32+22=V13S{GABCD=ABXBC=3X2=6•.,çBEFG9ᵫçABCDk(0,n2+n)ூᑖ᪆௃᪷îïᦪᑖð)04ஹAiBy,A2B2……Ḅ3᪆Ë:ᓽ)AòA2ஹP3…Ḅᙶ᪗:)õö,÷-)

17k+b.=1k=-lb,u;:3)b1=2•AiPiḄ᪆y=-x+2,y=-x+223](-2,4),y=^ABX//OA\29B\PiḄ᪆y=x+b2f:.-2+!=4,.,.!=6,.PI(0,6),y=x+62A2(3,9)y=xA\BiḄ᪆y=-x+b,3.-3+8=9,.b3=12,.P3(0,12),:.P”(0,n2+n),ᦑ'ᫀ(0,n2+n).ூ+,௃.⚪ὃ12345ᦪḄឋ8345ᦪ9:;+Ḅᙶ᪗ᱯ?@ABᦪCD45ᦪḄ᪆᪷FD45ᦪ9:;+Ḅᙶ᪗ᱯ?GHIJ⚪ḄᐵL.Mஹ'⚪(ᐳ66ᑖ)19ஹ(1)Q᪆R(2)Q᪆ூ᪆௃S⚪ᑖ᪆T(1)ᙊᑁWXYZḄ[\]⊡.(2)_ᡠ[Ḅᙊᕜ\J\.S⚪᪆T(1)᝞9জNPᓽᡠ.(2)᝞9ঝNC8Qᓽᡠ.

18AA+,TᙊᑁWXYZḄ[\]⊡._ᡠ[Ḅᙊᕜ\J\.20ஹi1jklQ᪆Ri2jBF=2DGᳮᵫQ᪆Ri3j75+1.ூᑖ᪆௃i1jᵫ_ᡠ[ᙊᕜ\qr90stNA£0=90°,wx᧕kNCDE=NB,}᪷FA4sᓽtklCDE%ABDi2jᵫARD,2DE=DB,wxt="BE,}ᵫᡠ[ᙊᕜ\qtZDAG^ZDEB,}ᑖklNBOGuNDBE,NGFD=NGDF,xtZ5G=GF=G8,ᓽt⚪Ri3j^CD=AB=y,DE=DB=z,ᵫDE//BC,t=%,t;ᓃ^,ᵫDE//BC,tBCCB2DEEFDF237==^^=M/;DF=2k,AF==1+>k,᪷Fᡠ.G=E>FMF2=M-6A•C=2k«l+EAk,BABFAF1+V5Gᦇᓽt⚪.ூ௃Ti1jklT•.•4jJ_.ZAED=90°.ZCED=90°,VADA.BC,:.ZADB=NCED=90஺,vZR4C=90°,:.DEHBC,..ZCDE^ZB,•••CE=A£),.,.CZ)^=AASZ)(AAS).(2)¡¢TBF=2DG.ᳮᵫ᝞£:ᵫi1jtTKDE/AABD,.DE=DB,:.NDEB=ZDBE,•.•A£)J_

19.\ZAGD=90°.ZAZX?+ZZMG=90°,N8DG+NADG=90஺../BDG=/DAG,••AG=AG8:.ZDEB=ZDAG,.ZBDG=ZDBE:.DG=GB,•/ZDFG+ADBF=90°,ZFDG+ZBDG=90°9,\ZGFD=ZGDF9.DG=GF=GB9,BF=2DG.(3)TAB=CO=y,DE=DB=z,DEIIBC,DECD~AB~~CBzy=yy+z᦮ᳮy2-*-2=0,1+¦T1-75/.y=---------zᡈy=----------zi©ªj,22•DEIIBC,DEEFDF2"AB--AF_1+75Tᵫ(2)2FBF=2DG=2O,

20EF2-2&-1+:.EF=M-BVZDEB=ZDAG,ZEFD=ZAFG♦ADEF~/iG4/*EFDF••—)AFFG;DF=2k,A=(1+.᧼_®_2k'(1+য%—ᚗ8:.k=---2:.AD=DF+AF=y[5+18ூCD௃P⚪ᔠὃᙊlh^ᙊḄឋஹᑗḄឋஹᐰkRGḄᑨឋஹhRGḄᑨឋஹᑖᡂ"#ᳮk⚪Ḅᐵᮣᵨᡠ⚪ᑭᵨᦪ⚪YLὃ⚪.21ஹ(1)᪆<(2)DE=—.13ூᑖ᪆௃iY(1),ᵫᩩ+¡¢ᑮNB=NC,AABCkῪRGᑭᵨkῪRGḄឋ᧕¢AD_LBC,ZADC=90°¦§ᩭ=©¢ᑮNADC=NBED,ª«⚪=©[¬

21BDDEᵫ(1)ABDE^^CAD>:.---=---CAAD5DEaᓽn—=---1312AD£=-13ூ+,௃⚪ὃ1®M\ZḄᑨA°ឋ8⚪ᐵLᙠr²³ᑨAAᳮ.22ஹ(1)9Q᪆90°•135°,45°R(2)Mᑖ´ᑖJµ¶·¸¶55ூᑖ᪆௃(D᪷FqῪM\ZḄᑨAAᳮº᧕»G9ZRᵫqῪM\ZḄឋ8ᓽtGᔜ½⚔\Ḅsᦪ;(2)᪷FqῪM\ZḄᑨAA¿º᧕»G9ZN8=a,ᑣNOCB=NDC4=NE4C=a,ZAZ)£R=NAED=2a,ᑣAECSABOC,ACOS^ABCG[ÁYᡂÃÄAE=A£)=X,BD=CD=y,GÆÇÈÆÇᓽt.ூ௃T(1)É9᝞91ஹ92ᡠÊ:ᙠ91Ë;AD=CDZACD=ZA=45°ZADC=90°vAB=AC,ZA=45°ZA£)C=90°vAB=AC,ZA=45°NB=NACB=67.5°ZECD=67.5°-45°=22.5°:.DE=CEZEDC=ZECD=22.5°ZDEC=135°/./BED=4$

22ᓽM½qῪM\ZḄ⚔\ᑖ90°ஹ135°ஹ45°ᙠ92Ë...ZZ)E4=ZA=45°,.•.ZA£)E=90°,/DEC=135°
BC=DC,.•.NC08=N8=67.5°•.♦NBCD=45஺ᓽM½qῪM\ZḄ⚔\ᑖ90°ஹ135°ஹ45°(2)᝞93ᡠÊCDஹAEÌJᡠḄMᑖZB=c,ᑣ==ZADE=ZAED=2a,ÍAAECSABDCAAC*&ABC,AE=AD=x,BD=CD=y,,:AAECSABDC,3x:y=2:3VAACD^zMBC,/.2:x=(x+y):2,x:y=2:3ÆÇÈ2:x=(x+y):22Vio2Mx=-----x=-------5-T\(ÏЩÑ)3V103V10y58AE=ÒCD=55ᓽMᑖ´ᑖJµ¶·ᐸ⚓55

23AூCD௃P⚪hGḄᔠឋ⚪¯ὃkῪRGḄᑨឋஹkῪRGḄ°oஹhRGḄᑨឋஹ±²³kP⚪ὃ´µḄᳮ¶·^¸¹º»¶·ᔠឋ¼½ᨵ'©¿.1..323ஹ(1)—(2)Pn=—.i416ூᑖ᪆௃(1)ᑡ]⊤ÂÃÄᡠᨵ+¶ḄÅÆgÇᑮÈÉᳫḄËÌᦪᑭᵨᭆ᳛Ï)ᓽ+\<(2)Ç]ÐÑÒ]ḄÉᳫ᪗ÔḄkY6ḄËÌᦪgᑭᵨᭆ᳛Ï)ᓽ+\.ூ4௃B1234

241(1,1)(2,1)(3,1)(4,1)2(1,2)(2,2)(3,2)(4,2)3(1,3)(23)(3,3)(4,3)4(1,4)(2,4)(3,4)(4,4)Õᐳᨵ16×tØᐸË4×Ù4ÚḄÛᳫ᪗ÝD᪵,41\P=—=-R164(2)ᨵM×ßàT2+4=6,3+3=6,4+2=6,316ூ+,௃.⚪á⌕ὃ1ÄãCäåæçḄᭆ᳛²³ᑡ⊤Cᡈ»᪛í9îïᭆ᳛ðJ⚪ḄᐵL.49924ஹ(1)Q᪆R(2)R(1)OEḄ´ᑖ3ᡈ1.242AMAEூᑖ᪆௃(1)ᵫÃÄË⚗——=——Ftk,}kl=NDCEAEANt'ᫀR(2)ᐜkNA7VE=NE4c,NᔠZANE=NDCENOCE=NE4c,x‘D=——FtDCAD97AMAF49AE=8--=-,ᵫ(1)ZAEMPNDCE,F——=—,QMN==R22AEAN24(1)ᑖNENM=ZEAC·NENM=NECAÙ×ßàᑖt.ூ௃(1)klTTAEJAM·ANḄÃÄË⚗.AMAE"~AE~^NVZA=ZAZAEM=ZANEVNO=90°3ZDCE+ZDEC=90°•:EM±EC•-ZAEM+ZDEC^90

25:.ZAEM=ZDCE:.NANE=4DCEN2
BVAClNEÕᚖQ•••ZE4C+ZAE2V=9OVZBAC=90:.ZANE+ZAEN=9Q.ZANE^ZEACᵫ1
ZANE=NDCE:.NDCE=NEAC:.tanZ.DCE=tanADAC.DE_DC''~DC~~\D'DC=AB=6,AD=8,9rDE=-297AE=8--=-22ᵫ1
ZAEM=NDCEtanZAEM=tanZDCE.AMDE,,!"#…21..AM=—8..AMAE'~AE~~AN…14..AN=——349:.MN=—24

261
VZNME=ZMAE+ZAEM,ZAEC^ZD+ZDCENM4E=ND=90ᵫDZAEM=NDCE.ZAEC=ZNMEôAAEC°î+EஹMஹN⚔+ᡠÈᡂḄM\Z®Í1
NENM=NEAC,᝞9ZANE=NEAC9ᵫ2
TDE=-22
NENM=NECA,᝞9õ+EÉEWLAC,ᚖ÷+”ᵫ1
ZANE=NDCE:.ZECA=NDCE.HE=DCRtanNHAE=S=T=9AHAD8DE=3x,ᑣHE=3x,AH=4x,AE=5xAE+ø=49••5x+3x=8,x=lDE=3x=3

279ù;ᡠúOEḄ´ᑖDᡈL2ூ+,௃.⚪ὃ12®M\ZḄᑨAAᳮᑭᵨM\Z®îïᐵḄqþᐵBᩭ
MNDEḄ.-L+14(0Vx«8Ḅ᦮ᦪ)25ஹ(1)p=20x+200(()ீ1x!᦮ᦪ)"(2)y=\2'(3)ᙠ&1ᜩ()*1ᜩ├,-.10(8Vx410Ḅ᦮ᦪ)ᑮᨬᜧ)ᨬᜧ├,-24ᐗூᑖ᪆௃(1)8⊤:(Ḅᦪ;<=)2>?@ᦪ)ᵨBCDᦪEFGpHxḄ@ᦪᐵDJ"(2)2ᑖK@ᦪ)ᑭᵨBCDᦪEFGyHxḄ@ᦪᐵDJ"(3)᪷;├,-=├OX├,ᓫR)ᑡ@ᦪᐵDJ)TUVFGWX.ூY
௃(1)ᵫ⊤:[\F]^pHxḄ@ᦪᐵD2>?@ᦪ)_`
᪆J!^p=kx+b,\k+b=220a(1,220)(3,260)dᐭG^f)“h)3ᦇ+8=260᝕=206=200.".p=20x+200,.pHxḄ@ᦪᐵDJ!^p=20x+200(0VxWlx!᦮ᦪ)(2)জo0cxW8q)`yHxḄ
᪆J!^y=kx+b(k^0)\2k+b=13a(2,13)(8,1)dᐭG^,s)|8ᦇ+஺=10k——
G^“2,஺=14

28u
᪆J!^y=—ঝo8Vx<1q)j=l.-gx+14(0Vx48Ḅ᦮ᦪ)w<ᡠy^)Hx(x!᦮ᦪ)Ḅ@ᦪᐵDJ!^y=10(80,.•.o8VxWlq)w~xḄᜧᜧ).,.ox=lq)wᨵᨬᜧ{!^200X1+3=4.V3600<4,ᙠ&1ᜩ()*1ᜩ├,-.ᑮᨬᜧ)ᨬᜧ├,-24ᐗ.ூ௃⚪ὃ_?@ᦪḄឋᙠ▭(Ḅᵨ.ᨬᜧᑭḄ⚪ᑭ@ᦪḄឋᩭ
)ᡃ✌ᐜ⌕ᔛ⚪,CO)@ᦪ¡¢)ᯠ¤Wᔠ▭⌱§ᨬ¨Vᫀ.26ஹ(1)50"(2)ª
᪆ூᑖ᪆௃(1)᪷;ᙊᕜCᳮ¯°±Ḅ᜜)³Ὺ°±Ḅ]µ¶·¸ḄᣚºᓽFG"(2)᪷;ᙊḄᑁ½¾¿±ÀÁ⊡Ḅឋ¶·¸ÃºᓽFÄÅ.ூY
௃
:(1)NBAD=NBFC,ZBAD=ZBAC+ZCAD,ZBFC=ZBAC+ZABF,:.ZCAD=ZABFXVZCAD=ZCBD,/.ZABF=ZCBD...NABD=NFBC,ÆAB=AD:.ZABD=ZADB,.NCBF=ZADB,

29NCBF=/BCF,ZBFC=2ZDFC=80°,—=T=5஺஺.(2)×NCFD=a,ᑣZR4D=ZBFC=2a,.EFGABC஺ᙊḄᑁ¦EFGAZBAD+ZBCD=1S0°,ᓽZBCD=180°—2஺)=:.ZACD=ZACB,.ZACD^ZACB=90°-a.ZCFD+ZFCD=a+(90஺—a)=90°:.NCDF=90°,ᓽC£>_LOb.ூCD௃P⚪Ú⌕ὃᙊḄឋlRGឋᔠ⚪©¿〉L⚪Ḅᐵ¶Ýᮣᵨᙊ^RGḄឋd¿ḄÞ.