2020-2021学年广西河池市宜州区七年级（下）期中数学试卷（附答案详解）

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2020-2021

ᦪᔁ1.ᓄ—6
2ḄA.-5B.5C.±5D.252.ᨬ᪷!"bḄ#$%A.24B.16C.7D.\33.᝞'!ᙠAABC!AC=8,DEA/IBCḄ)*!ᑣDEḄ,-A.4B.5C.6D.34.ᑡ/0ᦪ!1%234565768,ḄA.5,12,13B.9,40,41C.3,4,5D.2,3,45.9:;74BCDḄᕜ,316,ᑣ;74BCDḄ8,3A.4B.8C.12D.26.᝞'!ᙠ=>?874BCD!@5*ACஹ8஺CDEF0,OA=3cm,⌕H=>?874BCD3I7!ᑣOBḄ,-3A.4cmB.3cmC.2cmD.1cm7.V3xV7=•8.JKᨬLMḄ᦮ᦪ.9.ᙠ=>?874BCD!P4=38஺!"IJ/C=10.9:I74BCDḄ☢R3"^cm2,SḄ,32&cm,ᑣSḄT3cm.11.᝞'!ᙠVW74BCD!E38BCḄF!XL4E.48=2,ᑣYEḄ,3.BE

112.᝞',4C3;74BCDḄ@5*.4஺=50஺,ᑣ/8ACḄᜧ]3______-.13.᝞'!ᙠ=☢45ᙶ᪗a!F4(-2,4)JF8(-10,0)bcḄde314.᝞'!FE=>?874BCDḄ8CDḄF!AD,BEḄf,*CDEFF,DF=3,DE=2,ᑣ=>?874BCDḄᕜ,3.15.ghi(kll)2+g.ghi(V8+V3)XV6-4^.16.m2⚓!ᐳ40⚓

217.᝞'!ᙠRtAABC!P4cB=90஺!C஺p8ABqḄ*,AC=4,CD=3.r458BCḄ,.18.aஹbஹcABCḄ6ᩩ8,!tuvw+(b-yz+(c-2|=0.r}iABC45657.19.᝞'!AC,BCCDEF0,AB//CD,AD//BC,E,Fᑖ஺B,஺஺ḄF!r}i?874FCE=>?87.R

320.'জஹ'ঝᙳ4X4ḄVW7!]VW7Ḅ8,ᙳ3I,]VW7Ḅ⚔FF!*4BḄFᙳᙠFq!ᙠḄᢥ⌕r'!Hᡠ'7Ḅ⚔FᙳᙠFq!1⌕rᑏ.(1)ᙠ'জAB3l8l=>?87(2)ᙠ'ঝAB3@5*lVW7ḄI7.21.᝞'!l᪷,-3120cmḄᩈḄ4ஹBaḼl᪷,-3180cmḄ!ᜓᙠqlFC,ᯠ¢£¤4!H¤4¢ḄJᩈ᪀ᡂl45657!ᨴSB3458!r¨F£ᑖᡂḄᔜᨵ«,¬m4⚓!ᐳ40⚓

422.᝞'!;74BCDḄ@5*AC,8஺CDEF஺!ᑖU®4ஹ஺F24஺ஹ஺஺Ḅᚖ*,ᚖ*DEF£(1)r}i?8740DEI7(2)ND4E=60°,AD=6,rBOḄ,.23.±ᨵlᙽ?87Ḅ³ᙢABCD,᝞'ᡠµ!᪥gᑜᙠ³ᙢq¸¹₝»!¼½¾ZB=90°,AB=3m,BC=4m,CD=12m,AD=13m.=W¿₝»◤⌕200ᐗ!Â᪥◤⌕ᢗÄ/ᐭ«ÇÈÉÊ₝»¬XD

524.᝞'!ᙠ=>?874BCD!FEᙠBCḄf,*q!EC=BC,XLDEஹAC.AC140EF4.(1)r}i?874CEDI7(2)XLBD,D4CEFF.4C=2AD,rNBDEḄ-ᦪ.25.᝞'!ᙠVW7ABCD!E848qḄF!XLCE,®F஺2DFJ.CE,ᑖDBC,CEEFFஹG.(1)r}iCE=DF(2)48=3,'▢ÜÝᑖḄ☢RÞJVW74BCCḄ☢Rbß32i3,ᑣADCGḄ☢R3,CG+DGḄ,326.᝞'!ᙠI7ABCD,AB=2,EஹFᑖ88CஹADqḄF!XLEFஹ£?87CEFDâEFᢚä!Cஹ஺Ḅ@åFᑖ3FGஹH,EGD84DEFM,f,HFD8BCEFN.(1)r}i?87EMFN;7(2)FN1BC,4Lᑏ?87EMFNḄlᩩ@5*Ḅ,;(3)EF=MF,rENḄ,.m6⚓!ᐳ40⚓

627.JᦪéqḄFll@åḄᦪA.êᦪB.ᨵᳮᦪC.ìᳮᦪD.VᦪJíᦪ28.ᙠ=☢45ᙶ᪗a!F42,-3
ᡠᙠḄî▲A.mlî▲B.mî▲C.m6î▲D.m?î▲29.ᙠᑡ'7!N1J42ð)5Ḅ30.ᑡghVñḄA.V3+V5=V8B.2V2-V2=1C.V8=±2D.V036=0.631.=☢45ᙶ᪗a!9:FP2,—l
,ᑣFPᑮxéḄdeA.2B.-2C.1D.-132.ᑡóVñḄA.4Ḅ=W᪷±2B.ᨬ]Ḅêᦪ0C.ìᳮᦪḄÞlìᳮᦪD.íᦪôᨵõW᪷33.ghi=A,l1+V2B.-y/2,+1C.V2+1D.-1—V234.ö÷ᐗø5ùúḄûüýþ!ᵫ“”ḄᦪᳮᦪḄᦪᓻ“”ᢣḄ!A."#$%&B.()*&C.+ᓱ-D../%035.᝞23454BC6ABAC=90°,AD1BC,ᑣ268⊤:;ᑮ=>Ḅ?@Ḅ>Aᨵ!ᩩ.

7A.6B.536.᝞2=>a஻b,41=52஺,A.128°B.38°C.48°D.52°37.X;Ya+4,3a-2!ᑮ\ᙶ᪗_Ḅ?@`aᑣ஺!A.3B.-0.5C.3ᡈ0.5D.1ᡈ0.538.᝞2X=>a//b,=>cᑖghaஹb`jᑣᨵ!A.41+42-43=180°B.zl+z3-Z2=180°C.41+42+43=180°D.N2+43-N1=180°39.᝞pqr⊤“5ᑡ2t”uv5,2!,wx“4ᑡ3t”uy40.z{ᜧ}~-2—6,“<”ᡈ“=”!41.=434h\tḄᩩ᝞21=54°,2=°42.X;+3,m-3!ᙠ_ᑣm.43.᝞2=4ᙶ᪗64ஹB\;Ḅᙶ᪗ᑖgy3,1!,2,1!,ᑣᙶ᪗ᑁ;CḄᙶ᪗y.8⚓ᐳ40⚓

844.᝞2,345DEF=4345ABCḼBCᑮḄX4B=5cm,BE=2cm,DH=1cm,ᑣ26▢ᑖḄ☢ycm2.45.~-+-4!xVUZ.46.¡6xḄ¢~49ᔠ-1=24.

947.᝞2☢=4ᙶ᪗6;Ay(4,3),345¦BCᔣ¨5ᓫrª«1ᓫrᑮ345(1)¬34541/6®(2)ᑏ;y,BiCiḄᙶ᪗®(3)=±ᑏ345yB1GḄ☢~S=48.´ᗐ¶·¸¹~ºᙠ»>ᑏ¼½¾ᙠ¿À6Á·ᳮᵫ.ÃÄ~᝞2=>EFᑖgj48,C஺;E,F,41=42,4G=4”.¶~BEF+/.EFD=180°.¶·~Z.G=4H(ÃÄ)•••GE//()------=44(------)È~Z.1=42(ÃÄ):.z.1+z.3=z.2+Z.4ÊËJz/EF=.•••஻Î______)BEF+AEFD=180°()10⚓ᐳ40⚓

10AB49.᝞2ÃÄ;DஹEஹFஹGᙳᙠ345¦BCḄDEIIBC,42=43,GFLAB.¶~CDlAB.50.ÃÄÑᦪxḄ\ÓaḄÔ᪷ᑖg2a-14Öa+2,b+1Ḅ×Ô᪷y-3®cØḄ᦮ᦪᑖ®(1)ÚÖbḄ¢;

11(2)¡Üa-b+cḄ¢=®(3)Ýᑨßàᦪ(“ᨵᳮ”ᡈ“ᳮ”).51.᝞2345ADC6;BᙠAC4DjBEF,DE//BC.(1)XNC~4EDC=13,4cḄáᦪ;(2)X“=".¶~BE//CD.52.᝞2ᙠ☢=4ᙶ᪗6;B,CḄᙶ᪗ᑖgy(-a,2a),(3a,2a),ᐸ6a>0,;4yBCḄ6;BC=4,åæçᑡè⚪~(1)BCᡠᙠ=>hx_Ḅrᐵ®(2)aḄ¢¾ᑏ;4,CḄᙶ᪗®(3)ᙠy_ᔲîᙠ;P,ðñP4CḄ☢a5?XîᙠPḄᙶ᪗®XÓîᙠºó·ᳮᵫ.12⚓ᐳ40⚓

12

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ᑣ⚪ᐵ.2.ூᫀ௃Cூ᪆௃%4ஹ'a=24(ᑣ)=2eᦑA+,ᔠ⚪..Bஹ'a=16(ᑣW/=4,ᦑ8+,ᔠ⚪..Cஹ'a=7(ᑣ᜛ᨬ2᪷ᦑC,ᔠ⚪..Dஹ'a=|,ᑣ3=,ᦑ஺+,ᔠ⚪⚪..ᦑ⌱%C.ᨬ2᪷Ḅᩩ9%:1
;<=ᦪḄ?ᦪ᦮ᦪᡈBC?᦮D:2
;<=ᦪE+FᨵHᓄJK=ᦪᡈK=Ḅ?ᦪᡈ?.L⚪ὃᨬ2᪷⚪Ḅᐵᳮᨬ2᪷ḄNOL⚪PQRẠ⚪T.3.ூᫀ௃Aூ᪆௃U14⚓ᐳ40⚓

14%•DDE[ABCḄE_`•%*AC=4.ᦑ⌱%A.ᵫ0E[ABCḄE_`᪷efghE_`ḄឋjkDEḄlm.⚪ὃfghE_`Ḅឋj.⚪nom+ᜧq.ᦪhrᔠstḄuᵨ.4.ூᫀ௃Dூ᪆௃%A.-52+122=132,|5,12,13J}~ᡂgfghᦑL⌱⚗+,ᔠ⚪.DB.•:92+402=412,.••|9,40,41J}~ᡂgfghᦑL⌱⚗+,ᔠ⚪.DC-32+42=52,.••|3,4,5J}~ᡂgfghᦑL⌱⚗+,ᔠ⚪.D£).•••22+32*42,.•|2,3,4J}+~ᡂgfghᦑL⌱⚗,ᔠ⚪.Dᦑ⌱%D.ᐜᑖk}ḄK=ᨬlḄ}ḄK=ᔲᓽH.L⚪ὃNᳮḄ⌮Nᳮq.%᝞fghḄ}aஹbḄK=QUf}cḄK=fghgfgh.5.ூᫀ௃Aூ᪆௃%•••hḄ}hḄᕜlJ16,hḄ}lJ4,

15ᦑ⌱%A.᪷ehḄ}ᓽH.⚪ὃhḄឋjᐵ᪷ehḄ}.6.ூᫀ௃Bூ᪆௃%•••}hABCDK¢}h•••AC=20A=6(cm),OB=OD,⌕£K¢}h4BC஺¤hᑣBD=AC=6cm,•••OB~^BD=3(cm),ᦑ⌱%B.ᵫK¢}hḄឋj4c=6(cm),⌕£K¢}h4BCD¤hᑣB஺=AC=6cm,ᓽHk.L⚪ὃ¤hḄᑨNK¢}hḄឋj¦§¨©¤hḄᑨN⚪Ḅᐵ.7.ூᫀ௃V21ூ᪆௃%V3xV?=V21-ᦑᫀJ%V21.ªᑭᵨ᪷Ḅឋj
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ᑣ⚪ᐵ.8.ூᫀ௃U16⚓ᐳ40⚓

165ூ᪆௃%•••16<23<25,4

17%V48^2V2=V6(cm).ᦑᫀJ%V6.᪷el=hḄ☢¼½Hkl=hḄ¾.L⚪ὃ᪷Ḅuᵨᐵ¨©l=hḄ☢¼½.11.ூᫀ௃V5ூ᪆௃%ᙠ=h4BCDEAB=BC=2,Z.B=90°,JBCEÀ,.BE=CE=1,AE=y1AB2+BE2=ÁᦑᫀJ%V5-᪷e⚪.H¦48=2,BE=1,NᳮᓽHkr.L⚪ὃ=hḄឋj¨©=h}ஹgJgḄឋj⚪ᐵ.12.ூᫀ௃65ூ᪆௃%•••}hABCDh1•DC//AB,Z-BAC=:4DAB,vD=50°,••/.DAB=130°,•••Z.BAC=65°,ᦑᫀJ%65.᪷ehḄឋjHDC஻/IB,^BAC=AB,ᑭᵨK¢`ḄឋjH4ZMB=130°,ÃÁHᫀ.U18⚓ᐳ40⚓

18⚪⌕ὃhḄឋjᐵhḄᩩÄg`ÅᚖÇÈÉᩩÄg`KᑖÄg.13.ூᫀ௃4V5ூ᪆௃%•••À4(-2,4),ÀB(-10,0),•••À4°ÀBÌÍḄÎÏJJ(-2+10)2+42=4V5.ᦑᫀJ%4V5.L⚪ªᵨÀÍÎϽᓽHᫀ.L⚪⌕ὃK☢gᙶ᪗ÓEÀḄÎϽªᵨÀÍÎϽᓽH.14.ூᫀ௃14ூ᪆௃%•••}h4BCDK¢}h.AB=CD,AD=BC,AD//BC,:.CBE=F,CDḄEÀ:•CE=DE=2,CD=2DE=4,ZCBE=FᙠABCEAFDEE\^BEC=/.FED,CE=DE.•.[BCEf[FDE(AAS),BC=DF=3,K¢}hABCOḄᕜl=2(BC+CD)=2x(3+4)=14DᦑᫀJ%14.ᵫK¢}hḄឋj4B=CD,AD=BC,AD//BC,Ø4CBE=NF,ᵫ4AS■ØÚfAFOE,BC=DF=3,ᓽHkK¢}hABC஺Ḅᕜl.

19L⚪ὃK¢}hḄឋjஹᐰfghḄᑨN°ឋjஹK¢}hᕜlḄ
D¨©K¢}hḄឋjÇ~âÜᳮ
ÝÞ⚪Ḅᐵ.15.ூᫀ௃%ß=3+1-2à+2à=4.ூ᪆௃ªᑭᵨáᐰK=½ஹ᪷Ḅឋjᓄ2ÃÁᔠÇᫀ.⚪⌕ὃ᪷Ḅâᔠ
ᓄ2᪷⚪ᐵ.16.ூᫀ௃%ß=2ã+äåxæ2ã=2>/2xV6+V3xV6-2V2=4V3+3V2-2V2=4V3+\[2.ூ᪆௃ᐜçᔜ᪷ᓄJᨬ2᪷â᪷Ḅ
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ᯠëᔠÇíî᪷.17.ூᫀ௃%ᙠRM4BCECDï}4BðḄE`:.AB=2CD=6,ᵫNᳮBC=y/AB2-AC2=V62-42=2ñ.ூ᪆௃U20⚓ᐳ40⚓

20᪷egfghḄឋjk4B,᪷eNᳮ
ᑮᫀ.L⚪ὃḄgfghḄឋjஹNᳮᙠgfghEï}ðḄE`Qï}Ḅò⚪Ḅᐵ.18.ூᫀ௃ØÚ%ᵫ⚪.%a—1=0,b—6=0,c—2=0,;a=1,b=,c=2,a2+b2=I2+(V3)2=4>c2=22=4,:.a2+b2=c2,•.[ABCgfgh.ூ᪆௃᪷eᏔ=
ôK=᪷Ḅõöឋka,b,cḄ÷ᯠëᑭᵨNᳮḄ⌮Nᳮâ
ᓽH.L⚪ὃNᳮḄ⌮Nᳮ¨©NᳮḄ⌮Nᳮ⚪Ḅᐵ.19.ூᫀ௃ØÚ%AD“BC,}h4BCDK¢}h•••OA—OC,OB——OD.•••E,FᑖOB,஺஺ḄEÀ11OE=-OB,OF=-OD,22OE=OF,}h4FCEK¢}h.ூ᪆௃ᵫᩩ94B஻CD,AD஻BCHØᑮ}h4BCDK¢}h᪷eK¢}hḄឋjH(M=OC,OB=OD,⌕Ø}h4FCEK¢}hø◤ØOE=OFᓽH.

21L⚪⌕ὃK¢}hḄᑨN°ឋjஹ`úEÀḄNO¦§K¢}hḄᑨNûüý◤rᔠᩩ9⌱þᔠ〉Ḅᑨ⚪ᩩᨵᐵᦑ⌱ᑖḄᑨ.20.ூᫀ௃#$(1)᝞'জ)4BC஺ᓽ,ᡠ.;(2)᝞'ঝঞ),4EBFᡈ4G8Hᓽ,ᡠ..ூ#᪆௃(1)᪷6Ḅ789'ᓽ:;(2)᪷6<Ḅ7=>⚪?Ḅ⌕.89'ᓽ:.⚪ὃBC'-EᵨGHC'ḄᑨIឋK<ḄᑨIឋKLMN,#⚪ḄᐵOᮣQRᵨᡠSMN#TU⚪.21.ூᫀ௃#$VM᝞'$GAC=xcm,ᑣBC=(180—x)cm,ᵫYZᳮ\$1202=X2+(180-X)2,]^#;#\$_=40ᡈ30,b4C,cᑣ1202+(180-x)2=#\$x=130;bBC,cᑣ1202+M=(180-x)2,#\$x=50.d22⚓ᐳ40⚓

22ᦑghijkᑖᡂḄmnᔜᨵ50cmᡈ130cm.ூ#᪆௃GpqrsḄjkᩈu᪀ᡂwgrxḄyz,hC,{Ijac+BC=180cm,GAC=xcm,ᑣBC=(180—x)cm,ᑭᵨYZᳮ}~]#]ᓽ:.9xḄ.⚪⌕ὃBYZᳮḄEᵨḄYZᳮcr#TU⚪ḄᐵO.22.ூᫀ௃(1)$•••BC஺AC1BD,Z.AOD=90°,vEA1AO,DE1DO,AEAO=^DOA=90°,40DE<;(2)#$•••ZODE<.-.AE//OD,/.ADO=/.DAE=60°,•••48CD•AB=AD,•4BDLx•BD=AD=6.ூ#᪆௃(1)ᵫḄឋK\AC•!"BD,ᑣ4஺஺=90°,4EAO==90஺ᓽ:\9;(2)ᵫ<ḄឋK\AE஻஺஺ᑣ4D஺==60஺ᵫḄឋK\4B=4஺ᑣ4BCLxᓽ:\9ᫀ.⚪ὃBḄ<ḄᑨឋKஹḄឋKឋKஹLxḄᑨឋKLMN;

23<ḄᑨឋKIḄឋK#⚪ḄᐵO.23.ூᫀ௃vB=90°,AB=3m,BC=4m,CD=12m,AC2=AB2+BC2=32+42=25,ᓽ4c=5m,AC2+CD2=25+144=169=132XvAD2=132,AC2+CD2=AD2Z.ACD=90°,••.ACDrx4BCDḄ☢=^x3x4+ix5xl2=6+30=36(m2),S᪥⌕ᢗᐭ,$200x36=7200(ᐗ);$S᪥◤⌕ᢗᐭ7200ᐗ¢₝¤.ூ#᪆௃⚪⌕ὃBYZᳮ=>YZᳮḄ⌮ᳮ\94ACDrx#⚪ᐵO.r¦ᑭᵨYZᳮ.94C,ᑭᵨYZᳮḄ⌮ᳮ\9N4C஺=90°,ᑭᵨxḄ☢\9ᫀ.24.ூᫀ௃(1)$•••4BC0,AD=BC,AD//BC,vEC=BC,d24⚓ᐳ40⚓

24•AD=EC,•4CEDvAC1AD,•^DAC=90°,•4CED<;(2)#$§/8஺0)AC=2AF,AC=2AD,:.AD=AFtAZ.ADF=Z.AFDf••Z.DAC=90°,•••©4DFLῪrx^ADF=45°,ᵫ(1):M4CEC<Z.ADE=90°,•••BDE=AADE-AADF=90°-45°=45°.ூ#᪆௃(1)ᵫḄឋK\=BC,AD//BC,ACECᯠsND4C=90஺ᓽ:\9;(2)ᐜ4஺=AF,\440F=N4FD,©£>?LῪrx\/4DF=45஺ᯠsᵫ<ḄឋK\N4DE=90஺ᓽ:\9ᫀ.⚪ὃB<ḄᑨឋKஹḄᑨឋKஹLῪrxḄᑨឋKLMN<ḄᑨឋK#⚪ḄᐵO.25.ூᫀ௃ூ#᪆௃#$(1)ᙠ4BCO)CD=BC,DCF=XCBE=9Q°,vDF1CE,DFC+BCE=90°,

25•BCE+BEC=90°,•BEC=Z.CFD,.-.©DCF=ACBE(24?1S),ACE=DF;(2)•••▢¼½ᑖḄ☢4BCDḄ☢¾¿,2$3,▢¼½ᑖḄ☢,:x9=6Á½ᑖḄ☢,9-6=3,,**'BCE(&CDFDCGḄ☢BEGFḄ☢Lᙳ,3=|,1OGDG=a,CG=b,{ÄJ^ab=X-a2+b2=32,a2+2ab+b2=9+6=15,ᓽ(a+b)2=15,•■a+b=V15ᓽCG+CG=V15,ᦑᫀ,$pV15.(1)©DC/x©CBEᓽ:;(2)᪷6ᐰL:\mᙽÁ½ᑖ☢Lᓽ:.9ADCGḄ☢ᔠYZᳮ:.9DG+CGḄ.⚪ὃBḄឋKḄឋK>“ᓝÊ”ÌÍ#⚪ᐵO.26.ூᫀ௃#$(1):᪷6ᢚÏ*HF஻GE,FN//ME,•••ABC஺<AD//BC,•••MF//EN,MENÐ4MFE=Z.FEN,Z.FEN=Z.FEM,Z.MFE=Z.FEM,d26⚓ᐳ40⚓

26ME=MF,MENÐ.(2)bFN1BC,ᑣMENF,■■AB=2,.FN=2,Ñ,2~.(3)ÒEF=MFÓ•••MF-ME,••©EMFLÔx,•••EMF=60°,CEK14CÕhK,᝞'ᡠÖ,GMK=x,ᑣME=2x,KE=2,ᙠRtAMEK)᪷6YZᳮ\,4x2=x2+4,#\x=×3EN=ME=2x=3ூ#᪆௃(1)᪷6ᢚÏ᧕\MENFME=MF,ᓽ:\;(2)ÒFN1BCÓEMFNÑ,ÐN=DC=2,ÙÚ.#ᓽ:;(3)ÒEF=MFÓAMEFLxCEK1ADÕhK,ᙠRtaMEK)ᵨYZᳮᓽ:.9ME,ÙÚ.9ENḄÑ.⚪ὃBᱯÜḄḄᢚÏU⚪ᱯÜḄឋKIᑨ#T⚪ḄᐵO.27.ூᫀ௃A

27ூ#᪆௃#$ÝᦪᦪßàḄhwwEᦑ⌱$A.᪷6ÝᦪᦪßàḄhwwE\9ᫀᓽ:.⚪⌕ὃBÝᦪᦪßḄᐵá#⚪ḄᐵOᙠÕÝᦪ:=ᙠᦪßàwwE⊤Ö9ᩭ.28.ூᫀ௃Dூ#᪆௃#$h4(2,-3)ᡠᙠḄä▲dä▲.ᦑ⌱$D.᪷6ᔜä▲ᑁhḄᙶ᪗ᱯé#ᓽ:.⚪ὃBᔜä▲ᑁhḄᙶ᪗Ḅêëᱯéìᔜä▲ᑁhḄᙶ᪗Ḅêë#TḄᐵO,gä▲Ḅêëᱯhᑖí$dwä▲(+,+);dä▲(-,+);dxä▲(w,-);dä▲(+,-).29.ூᫀ௃Cூ#᪆௃#$᪷6ïyḄ7:MᫀCᦑ⌱C.ïyð$mgñᙠòḄïóôᑖíᜐᙠöòḄmᩩrï÷ḄyzḄ.⚪ὃBïy#ø⚪xùᐵO:r¦Ùòᐭú.☢ûü)ᭆþḄᳮ#w⌕ÿᡷᭆḄᐵ⌕ᑮᳮḄ28⚓ᐳ40⚓

28Ḅ⊤⌕ᳮᡠᒹ#Ḅ$.30.ூ'ᫀ௃Dூ᪆௃+A.ᡃ-⍩/ᔠ1ᡠ24⌱⚗5ᔠ⚪7B.2V2-V2=V2.ᡠ2B⌱⚗5ᔠ⚪7C.89=2,ᡠ2C⌱⚗5ᔠ⚪7D89=0.6,ᡠ2஺⌱⚗5ᔠ⚪.ᦑ⌱+D.᪷=ᔠ1>⚗?@᪷ABC@᪷ḄD$ᓽFG.H⚪ὃJKᔠ1>⚗?@᪷ABC@᪷LMNOᔠ1>⚗?@᪷ABC@᪷ḄPAQRS⚪Ḅᐵ.31.ூ'ᫀ௃Cூ᪆௃+TPᑮxUḄVWQ|Y1|=1,ᦑ⌱+C.᪷=TᑮxUḄVWZTḄ[ᙶ᪗Ḅ^_F`'ᫀ.H⚪ὃJḄQTḄᙶ᪗Ḅ$+TᑮxUḄVWZTḄ[ᙶ᪗Ḅ^_a᝞UḄVWZTḄcᙶ᪗Ḅ^_.32.ூ'ᫀ௃Aூ᪆௃

29+44ḄC@᪷Q±2,ᦑH⌱⚗5ᔠ⚪7AiᨵᨬlḄmᦪᦑH⌱⚗5ᔠ⚪7C.7r+(-7r)=O,0QᨵᳮᦪQyᳮᦪᓽz{yᳮᦪḄ|YDQyᳮᦪᦑH⌱⚗5ᔠ⚪7D~ᦪᨵY{~Ḅ?@᪷ᦑH⌱⚗5ᔠ⚪7ᦑ⌱+A.ᑭᵨC@᪷ḄD$ᑨ4⌱⚗7᪷=mᦪḄD$-ᜧlᑨB⌱⚗7᪷=yᳮᦪḄD$PAᑨC⌱⚗7᪷=?@᪷ḄD$ᑨ஺⌱⚗.H⚪ὃJKmᦪḄD$-ᜧlC@᪷ஹ?@᪷ḄD$yᳮᦪḄD$-PAQẠᓫ.33.ூ'ᫀ௃Aூ᪆௃ft?+V2>11-V2<0,|1-V2|=V2-1.ᦑ⌱:A.᪷=^_ḄឋAF`'ᫀ.⚪ὃJḄQmᦪḄឋNO^_ḄឋQR⚪Ḅᐵ.34.ூ'ᫀ௃Bூ᪆௃+¡¢ᐗ¤5¦§Ḅ¨©ª«¬ᐸᨵY®¯°©±²³Ḅᦪ´µ¶·¸¹º,»¸Kᦪ´¼½ḄY¾ᦪ´ᓻÀ.ᦑ⌱+B.¡¢ᐗ¤5¦§Ḅ¨©ª«¬ᐸᨵY®¯°©±²³Ḅᦪ´µ¶·¸¹Á»¸30⚓ᐳ40⚓

30Kᦪ´¼½ḄY¾ᦪ´ᓻÀ.H⚪Â⌕ὃJKyᳮᦪL៉ᦪ´ᦻᓄQRH⚪Ḅᐵ.35.ூ'ᫀ௃Bூ᪆௃+TCᑮABḄVWQÆÇAC,TcᑮanḄVWQÆÇCD,T4ᑮBCḄVWQÆÇAC,TBᑮ4஺ḄVWQÆÇ8D,TBᑮACḄVWQÆÇAB,ᦑ⌱+B.᪷=TᑮÆḄVWḄD$`ÈÉ.H⚪ὃJKTᑮÆḄVWᳮTᑮÆḄVWQRH⚪Ḅᐵ.36.ூ'ᫀ௃Dூ᪆௃+᝞Ê,v41=43,41=52°,•••Z3=52°,•1,a//b,••Z.2=Z.3—52°,ᦑ⌱+D.

31᪷=CÆḄឋGᓽF.⚪ὃJKCÆḄឋLË“zÆC®ÍÎÏ”Q⚪Ḅᐵ.37.ூ'ᫀ௃Cூ᪆௃:᪷=⚪`|a+4|=|3a-2|,Ña+4=±(3a-2),•••a=3ᡈa=—0.5,ᦑ⌱+C.ᵫÔT4(a+4,3a-2)ᑮzᙶ᪗UḄVWÎÏᑣTPḄcஹ[ᙶ᪗Ḅ^_ÎÏᓽ|a+4|=|3a-2|,ᯠ×Ø^_ஹ@Ù`ᑮaḄ_ÚÛDPTᙶ᪗.H⚪ὃJKTḄᙶ᪗ÜÝ⚪Þßàᑡâ^_@ÙQ⚪ḄᐵãTᙠÔå^_@ÙæᓄZYç@Ùᯠ×G.38.ூ'ᫀ௃Dூ᪆௃+•••z3=z4,•••z4=zl+z5=(180°-42)+zl,•••Z3=180஺-42+41,42+43-41=180°,ᦑ⌱+D.32⚓ᐳ40⚓

32᪷=CÆḄឋ2èÍé᜜ÍḄឋᓽF`âÈÉ.H⚪ὃJḄQèÍéᑁÍ-᜜ÍḄᐵìCÆḄឋ'⚪ḄᐵQL2í+জzÆC®ÍÎÏ7ঝèÍéḄY{᜜ÍÏÔ-ðÎñḄz{ᑁÍḄ|.39.ூ'ᫀ௃(4,3)ூ᪆௃+•••“5ᑡ2”Ëô(5,2),“4ᑡ3”ËZ(4,3).ᦑ'ᫀZ+(4,3).᪷=Y{ᦪ⊤õᑡᦪÑ{ᦪ⊤õᦪᑏâᓽF.H⚪ὃJKᙶ᪗D®÷ᳮᨵøᦪḄz{ᦪḄm▭$Q⚪Ḅᐵ.40ூ'ᫀ௃>ூ᪆௃+•••|Y2|=2,1-751=75.Û6>2.—2>—V5-ᦑ'ᫀZ>.ᐜAzᦪḄ^_`ᑮ|-2|=2,|-V5|=V5,ᵫÔ⌲>2,᪷=~ᦪḄ^_þᜧÿᦪᓽᑮ-2-Ḅᜧᐵ.⚪ὃᦪᜧᡠᨵᦪᜧ0,ᡠᨵ"ᦪ0#"ᦪḄ$%&ᜧ'(ᦪ.41.ூ,ᫀ௃

3336ூ0᪆௃0᝞3'vZ1=54°,Z.FEG=90°,•43=36°,•:AB"CD,•z2=z3=36°.ᦑ,ᫀ536.ᐜ᪷841=54°,FEG=90°,943=36°,:᪷8;<=Ḅឋ?'942Ḅ@ᦪ.⚪A⌕ὃḄC;<=Ḅឋ?'0DE⚪ḄᐵFCGHIJ=;<'KLMNO.42.ூ,ᫀ௃3ூ0᪆௃0•:R4(S+3,??1-3)ᙠᑐWX'm—3=0,0m=3.ᦑ,ᫀ53.JYᑭᵨ\WXRḄᙶ᪗ᱯR`aḄ&.b⚪A⌕ὃRḄᙶ᪗'cdexWXRḄᙶ᪗ᱯRC0⚪ᐵF.43.ூ,ᫀ௃(-1.3)ூ0᪆௃f34⚓'ᐳ40⚓

340RCḄᙶ᪗5(—1,3).ᦑ,ᫀ5(—1,3).✌ᐜ᪷84Rᙶ᪗cklRLm'ᯠo:pqᙶ᪗':ckCRᙶ᪗ᓽ.b⚪A⌕ὃRḄᙶ᪗'ᐵFCcpqᙶ᪗.44.ூ,ᫀ௃9ூ0᪆௃0•••JMrMsABCtḼBCvᔣ;xᑮJMrMsDEF,:.BE=2cm,DE=AB=5cm,'ABC=.t^DEF,•.EH=5-1=4(cm),S^=S,ABCADEF•▢z{ᑖḄ☢~=S-.ABEH=+AB)xBE=x(4+5)x2=9(cm2).ᦑ,ᫀ59.ᑭᵨ;xḄឋ?ᑮBE=2cm,DE=AB=5cm,ABCrDEF,:᪷8☢~Ḅᑮ▢z{ᑖḄ☢~=S-.ABEHᯠoᑭᵨsḄ☢~ᓽ.⚪ὃ;xḄឋ?3s᦮tJ=vᔣx'ᑮḄ3s,3sl3sḄsᜧᐰNK#3sḄR'Cᵫl3sḄRxoᑮḄ'(IRC%R.Yᔜ%RḄ=;

350l=-1+3+4x05=-1+3+2=4.ூ0᪆௃JYᑭᵨqv᪷Ḅឋ?᪷Ḅឋ?ᑖ¡ᓄ£'¤ᑭᵨᨵᳮᦪḄ¦ᔠ¨©ᑣ`,ᫀ.b⚪A⌕ὃᦪḄ¨'cᓄ£ᔜᦪC0⚪ᐵF.46.ூ,ᫀ௃049/=25,ூ0᪆௃᪷8;v᪷Ḅ«¬'¤<ᓽ0,.⚪ὃ;v᪷'®GH;v᪷Ḅ«¬C0⚪ḄᐵF.47.ூ,ᫀ௃2.5ூ0᪆௃

36বS=2x3Wxlx3/x2xlqxlx2=25ᦑ,ᫀ52.5.1
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JYᑭᵨrMs5BiG'ᡠᙠ±s☢~²³ᕜµrMs☢~`,ᫀ.b⚪A⌕ὃ;x¶ᣚrMs☢~9©'c`%RLmC0⚪ᐵ¸.48.ூ,ᫀ௃FHᑁ┯MNO'IJ=;<43IJ=;<'ᑁ┯MNOEFDABᑁ┯MNO,IJ=;

37vz2=Z3,:.zl+z2=90°.:./.ADC=90°.ACD1AB.ூ0᪆௃᪷8஺E஻BCÆ41=NB,¤Æ48+N3=41+43=90஺':ᵫN2=N3Æ41+42=90஺'¤¾¿.⚪ὃ;<=Ḅឋ?'0⚪ᐵFCÍᔠ3sᮣϨᵨ;<=Ḅឋ?¤Ḅ᦮ᦪ{ᑖC2,c-2»d—b+c=4—(—28)+2=34,ᦑ,ᫀ534#(3)Ða=4,c=2Ñ'f38⚓'ᐳ40⚓

38\l2ac=V2x4x2=V16=4>42acCᨵᳮᦪ,ᦑ,ᫀ5ᨵᳮ.(1)᪷8;v᪷Ḅ«¬(2a—14)+(a+2)=0,Ù9`aḄ&'¤9`\Ḅ&'᪷8qv᪷Ḅ«¬b+1=-27,Ù9`bḄ&#(2)Ü`6Ḅ&'Ù9`cḄ&'ᯠoÝᐭߤ<ᓽ0,#(3)a,cḄ&Ýᐭߤ<'ᓽᑨá.⚪ὃÜâᳮᦪḄᜧ';v᪷'qv᪷'®GH;v᪷'qv᪷Ḅ«¬C0⚪ḄᐵF.51.ூ,ᫀ௃0(1)vDE//BC,C+EDC=180°,•••zCZ.EDC=13,:.Z.EDC=3Z.C,ZC+3ZC=180°,C=45°#(2)vDE//BC,C+4EDC=180°,vZ.C=Z.E,4E+4EDC=180°,•••BEHCD.ூ0᪆௃(1)᪷8“IJ=;<'K»ᑁM¼⊡”ᓽ0#(2)ᵫ;<=Ḅឋ?ᑮ“+EDC=180°,OíÝᣚᑮNE+EDC=180°,ᓽᑨkBE஻Mb⚪ὃ;<=Ḅᑨkឋ?'®GH;<=Ḅᑨkkᳮឋ?kᳮC0⚪ḄᐵF.52.ூ,ᫀ௃

39;<ூ0᪆௃0(1);<':BCḄñᙶ᪗NK'•••BC//XW'ᦑ,ᫀ5;<#(2)•••BC=4,'•3u—(—a)—4,•Q=1,8(-1,2),C(3,2),”5ḄR'•ò1,2)#(3)óᙠ'ôP(O,m),•AC=2,x2x|m-2|=5,•••m--3ᡈ7,•••P(0,-3)ᡈ(0,7).(1)ᵫBCḄñᙶ᪗NK'ÆBC஻xW#(2)ᵫR8,CḄᙶ᪗ᑖ¡5(-a,2a)ஹ(3a,2a),BC=4ᓽ9`aḄ&'ᓽ`BCḄᙶ᪗':ᵫ45BCḄRᓽ9`4Ḅᙶ᪗#(3)ôP(0,m),ᑭᵨrMsḄ☢~ᓽ`Í÷.⚪A⌕ὃ;☢JMᙶ᪗RḄᙶ᪗Ḅᱯø'rMsḄ☢~OÆù'®GHᙶ᪗3sḄᐵC0⚪ḄᐵF.f40⚓'ᐳ40⚓