2018年中考数学提分训练

2018年中考数学提分训练

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时间:2023-03-17

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21VAc=AP,JZAPc=ZAcP,VZBPc+ZAPc=180°AZBPc+ZAcP=180°,••ᵬ┯Ênã:᝞2,VAB±PB,Ac±Pc,AZABP=ZAcP=90°,AZBPc+ZA=180°,ãÒᦑ§ᫀbD.ூᑖ᪆௃ᵬb᪷\Ûd¥ÛSÖßNAPc=NAcP,ᵫ@SḄØæÖßNBPc+NAPc=180°,ÛçèéᓽÖᑨ²nãb᪷\wdxḄᑁS?ÖpãḄ7Ò஺5.ூ§ᫀ௃Bூ¦᪆௃btucD,•••ᙠAABc=ZAcB=90°,ZA=30°,Bc=4,:.AB=2Bc=8.••7ÖpBe=cD=4,cEAiBDḄᚖ>@ᑖAcDêdABḄ=A••BD=AD=4,

22ABF=DF=2,AAF=AD+DF=4+2=6.ᦑ⌱B.ூᑖ᪆௃tucD,᪷\ᙠAABc=NAcB=90°,ZA=30°,Bc=4ÖpAB=2Bc=8,ᵫ7ÖpBc=cD=4,cEAiBDḄᚖ>@ᑖAᦑcDêdABḄ=A\ëÖß_BDḄ#ìíÖß_`a.6.ூ§ᫀ௃Dூ¦᪆௃᝞জBᙊBe#$%&'+AB-D,ABeDÜÛῪRSxnঝAᙊAc#$%&'+AB-E,AAcEÜÛῪRSxnঞcᙊBe#$%&'+Ac-F,ABcFÜÛῪRSxnটAcḄᚖ>@ᑖA+AB-H,aAcHÜÛῪRSxnঠABḄᚖ>@ᑖA+Ac-G,ᑣ4AGBÛῪRSx;ডBeḄᚖ>@ᑖA+AB-I,ᑣABcIÛῪRSx.ᦑ§ᫀbc.

23ூᑖ᪆௃᪷\ÛῪRSxḄឋÔᑖóô&_xᓽÖß_§ᫀ஺7.ூ§ᫀ௃Dூ¦᪆௃bᙠopRSxABc=«ABᡠᙠḄ>Axö«¥÷öcoyö&¥ùḄXöஹyrö,Nx'o'y'=45°,3bᙠx'öe«o'A'=oA,o'B'=oB,ᙠy'öe«o'c'=oc,RbtuA'c',B'c',ᡠßRSxA'B'c'ÜRSxABcḄ>û᪷\&RSxḄ>ûḄU7Öpë⚪⌱D,ᦑ§ᫀbD.ூᑖ᪆௃᪷\&RSxḄ>ûḄU7Öß_§ᫀ஺8.ூ§ᫀ௃Dூ¦᪆௃᝞tucDஹ••ᙠ¨coD?¨=9.,.¨coD^A(SSS),:.ZAoB=ᦑ§ᫀbDoூᑖ᪆௃᪷\ᐰÛRSxḄᑨØU7SSS,&_RSx.

249.ூ§ᫀ௃Dூ¦᪆௃᪷\üýᡠজÒþNc=90஺ZB=30°,ᑣNBAc=60஺íAD@ᑖNBAc,ᑣNDAB=30°,ᡠNADc=NDAB+NB=60஺,ᡠঝÒnþNDAB=NB=30°,ᡠAABDÛῪRSxᡠᨵঞÒnþAD@ᑖNBAc,ᡠDᑮABAcḄlmsÛíDc±Ac,ᑣDᑮ>AABḄlmÛ-cDḄ#rᡠটÒ.ᦑ§ᫀbD.ூᑖ᪆௃(1)ᵫopSḄ@ᑖAḄ7pADNBAcḄ@ᑖAn(2)᪷\RSxḄ᜜ḄᑁḄNADc=NDAB+NB,ᵫ(DNDAB=30°,ᡠZADc=ZDAB+ZB=60°(3)ᵫ(2)#$ZDAB=30°=ZB,᪷&Ὺ()Ḅᑨ+AABD,Ὺ()(4)᪷&.ᑖ01Ḅ2ᑮ4Ḅ56$2Dᑮ70ABḄ56cDḄ89஺10.ூ>ᫀ௃DூA᪆௃CᵨEFGHGNAoc=NAoBḄJKL,2஺

25MᙊO$PQ8MRSTUজ$ᑖWXoAஹoB2EஹF,JZLḄGH[\ঝḄG^,2EMᙊO$EF8MRSTU.ᦑ⌱D.ூᑖ᪆௃᪷&GKK7ḄG^ᓽbcd.1Lூ>ᫀ௃BூA᪆௃CefEG,••ᵫGH#AD=AE,AG,NBADḄ.ᑖ0$AZ1=Z2,AAG±DE,oD=DE=3.Vh4)ABcD,.ih4)$••cD஻AB,AZ2=Z3,.\Z1=Z3,AAD=DG.VAG±DE,:.oA=AG.ᙠRtAAoDl$oA===4,••AG—2Ao—8.ᦑ⌱B.ூᑖ᪆௃efEG,ᵫGH#AD=AE,᪷&Ὺ()Ḅ

26ឋn#AG,DEḄᚖ7.ᑖ0$ᵫ.ih4)ḄឋnbcD஻AB,ᦑbN2=N3,&r#AD=DG,ᵫῪ()Ḅឋn#oA=AG,ᑭᵨtu+ᳮwboAḄ8ᓽ.12.ூ>ᫀ௃BூA᪆௃CecEF,AEyBFX2o,••h4)ABcD,.ih4)$AB=AF,••h4)ABEF,z)$AAE±BF,oB=BF=4,oA=AE.VAB=5,ᙠRtAAoBl,Ao==3,:.AE=2Ao=6.ᦑ⌱B.ூᑖ᪆௃ᵫGHᑮAB=AF,AG.ᑖNBAD,ᦑbh4)ABEF,z)$ᵫz)Ḅឋn#AE_LBF,ᦑboBḄ8$ᵫtu+ᳮᓽboAḄ8$bcd.Zஹ⚪13.ூ>ᫀ௃$70.iூA᪆௃᝞HᡠC᪷&⚪QbCZ1=Z2N1N2,;VZ1=Z2,

27a஻b$70.iᦑ>ᫀMC$70.i.ூᑖ᪆௃7E(ᡠGḄ,.$NlஹN2Ḅᜧ$,$“$70.i”.14.ூ>ᫀ௃PNPPN0ூA᪆௃C᝞HVPN±oB••0PNḄ8,⊤2Pᑮ70BoḄ56VP±oA••PḄ8,⊤2ᑮ70AoḄ56VoN±PN••0oNḄ8⊤2஺ᑮ70PNḄ56VP±oA•2Pᑮ70oAḄ56M0ᦑ>ᫀMCPNஹPஹPNஹ0ூᑖ᪆௃ᐜ᪷&⚪QTbH)$᪷&2ᑮ70Ḅ56Ḅ+$ᓽwA஺15.ூ>ᫀ௃10ூA᪆௃CᵫGH#cD,0ABḄlᚖ0$•••Ac=AD=Bc=BD,••h4)AcBD,z),

28VAB=4,cD=5,ASz)AcBD=XABXcD=X4X5=10,ᦑ>ᫀMC10.ூᑖ᪆௃ᵫGH#cD,0ABḄlᚖ0$h4)AcBD,z)$ᑭᵨSz)AcBD=XABXcDwAᓽ.16.ூ>ᫀ௃ூA᪆௃CᵫGH#$EFᚖ7.ᑖAB,ᓽDe,7()ABc41Ḅl0$ᦑDc=AB==X15=.ᦑ>ᫀMC.ூᑖ᪆௃ᵫGH#$EFᚖ7.ᑖAB,ᓽDe,7()ABc41Ḅl0$ᙠRtZ\ABcl$ᑭᵨtu+ᳮwbABḄ8$ᓽwDeḄ8஺17.ூ>ᫀ௃56ூA᪆௃C••h4)ABeDḄ¡)$AD஻Bc,AZDAc=ZAcB=68°.••ᵫG^#$AF,NDAcḄ.ᑖ0$AZEAF=ZDAc=34°.••ᵫG^#$EF,0AcḄᚖ7.ᑖ0$AZAEF=90°,AZAFE=90°-34°=56°,AZa=56°.

29ᦑ>ᫀMC56.ூᑖ᪆௃ᐜ᪷&¡)ḄឋnbAD஻Bc,ᦑbNDAcḄ9ᦪ$ᵫ.ᑖ0Ḅ+wbNEAFḄ9ᦪ$ᵫEF,0AcḄᚖ7.ᑖ0bNAEFḄ9ᦪ$᪷&()ᑁ+ᳮbNAFEḄ9ᦪ$bcd.18.ூ>ᫀ௃2ூA᪆௃C᪷&⚪lḄ¤¥GH¦☢ḄH$¨2DGDE±AcE,ᵫEFGHḄ©^ADMNBAcḄ.ᑖ0$ªMNADB=60஺,ᡠNB=90஺$ᵫ.ᑖ0ḄឋnBD=DE=2,ᙠRtz^ABDl$AB=BD*tanZADB=2.ᦑ>ᫀM2.ூᑖ᪆௃ᵫEFGH-.ᑖ0ḄG^ADMNBAcḄ.ᑖ0$ᵫ.ᑖ0ḄឋnBD=2,²#NADBᓽwbABḄ³.19.ூ>ᫀ௃2´µ2$N,efNXABP,ᑣ2PᓽMᡠwூA᪆௃Iᵫtu+ᳮABZ;

30(II)TAB,AP=,••9AAPCBP=2C1.´µ2$N,efNXABP,ᑣ2PᓽMᡠwVA/7BN,AAAP^ABNP,••9VA=2,BN=1,••9••P2¹ᔠ⚪Q.ᦑ>ᫀMC´µ2$N,efNXABP,ᑣ2PᓽMᡠw஺ூᑖ᪆௃(I)ᑭᵨtu+ᳮwbABḄ8஺(H)ᐜwbBPḄ8,»bAPCBP=2C1,´µ2,N,efNXABP,ᑣ2PᓽMᡠw$᪷&¼()Ḅᑨ++ᳮ$½APsaBNP,b¾¿4ᡂÁÂ$APCBP=2Clo20.ூ>ᫀ௃ூA᪆௃ூA>௃efAE,᪷&⚪Q#Nᚖ7.ᑖAc

31AAE=cE=3ᙠRtAADEl$AD2=AE2-DE2AD2=9-4=5VAc2=AD2+Dc2Ac2=5+25=30:.Ac=ூᑖ᪆௃᪷&GH$#Nᚖ7.ᑖAc,᪷&ᚖ7.ᑖ0Ḅឋn$wbAEḄ8$᪷&tu+ᳮwbADḄ8$ᯠÄᑭᵨtu+ᳮwbAcᓽ஺(ஹA>⚪21.ூ>ᫀ௃AC᝞Hᡠ$VZEAc=ZAcB,••AD஻cB,VAD=Bc,$h4)ABcD,.ih4)$•AB஻cD.ூA᪆௃ூᑖ᪆௃ᵨEFGHᓽÅᡂGH஺ᳮᵫ᝞¦C᪷&ᑁ┯$70.iAD஻cB,²#ADZBe,᪷&KǾ4.iÈḄh4),.ih4)h4)ABcD,.ih4)$᪷&.ih4)ḄឋnAB஻cD.22.ூ>ᫀ௃1᝞H1,B஺MᡠwGḄ.ᑖ0

322᝞H2,¨2஺GoD_LAB2D,VZAcB=90°,ᵫ1#Bo.ᑖNABc,.*.oc=oD,BD=BcoVAc=4,Bc=3AAB=5,BD=3,AD=2Éco=x,ᑣAo=4-x,oD=xᙠRtAAoDl$,$ᓽ2஺ᑮABḄ56MூA᪆௃ூᑖ᪆௃12BMᙊO$PQ89MRSTU,XBA,Be2$ᑖWÌX2MᙊO$ᜧÌX2ÍḄ56Ḅ89MRS$TU$ÎᙠᑁXK2$¨B2ÏÌ2$GÐ0B஺XAc2Ñ$Bo»,ᡠwḄNABcḄ.ᑖ02¨2஺GoD_LAB2D,᪷&.ᑖ01Ḅ2ᑮ4Ḅ56boc=oD,BD=Bc=3o᪷&tu+ᳮbABḄ8$bADḄ8$Éco=x,ᑣAo=4-x,oD=x,ᙠRtTXAoDl$ᑭᵨtu+ᳮb©Ô$wAb>ᫀ஺23.ூ>ᫀ௃1AC᝞H,Gb.ᑖ0coGb஺o.2ACAcy஺oᑗ.

33ூA᪆௃ூᑖ᪆௃(1)᪷&⚪QᐜGbNAcBḄ.ᑖ0$஺MᙊO$oBMRSTᙊᓽ஺(2)᪷&.ᑖ01Ḅ2ᑮ4Ḅ56Ïᑗ0Ḅᑨ++ᳮ$ᓽbAcy஺஺ᑗ஺24.ூ>ᫀ௃(1)AC᝞Hᡠ$70EFᓽMᡠw(2)AC••h4)ABcD,z)$AZABD=ZDBc=ZABc=75°,De//AB,ZA=Zc.AZABc=150°,ZABc+Zc=180°,AZc=ZA=30°,•EFᚖ7.ᑖ00AB,AAF=FB,AZA=ZFBA=30°,:.ZDBF=ZABD-ZFBE=45°ூA᪆௃ூᑖ᪆௃(1)ᑖWA,B2MᙊO$ᜧAB89KRḄ89MRSTU$UᙠABḄÖᑖWX$¨ÌX2G70$XAB2E,XAD2F,,70EFᓽMᡠw(2)᪷&z)ḄឋnbNABD=NDBc=NABc=75°,De஻AB,ZA=Zc.ᦑNABc=150°,ZABc+Zc=180°,Zc=ZA=30°,᪷&ᚖ7.ᑖ0ḄឋnbAF=FB,᪷&4¾ÏḄ×ᓽb>ᫀ஺

3425.ூ>ᫀ௃(1)AC᝞Hᡠ:(2)ACVZBAc=90°,Zc=30°••2DᙠAcḄᚖ7.ᑖ01$:.DA=Dc,.\ZcAD=Zc=30°,VZDEA=ZBAc=90°,AAABc^AEDA.ூA᪆௃ூᑖ᪆௃(1)ᑭᵨEFGHGbAcḄᚖ7.ᑖ0XBe2D,XAc2Eᓽ஺(2)᪷&ᚖ7.ᑖ0ḄឋnbDA=Dc,NcADZZe,ᯠÄ᪷&Ǿ¿Ḅ()¼$ᓽcd஺26.ூ>ᫀ௃(1)(2)জØCᙠAD1´K2FÙDF=Dc,efEF,♦DE.ᑖNADc,:.ZFDE=ZcDE,ᙠ4FEDacDEl$DF=Dc,ZFDE=ZcDE,DE=DEAAFED^AcDE(SAS),

35AZDFE=ZDcE=90°,ZAFE=180°-ZDFE=90°JZDEF=ZDEc,VAD=AB+cD,DF=Dc,.\AF=AB,ᙠRtAAFE^RtAABE(HL):.ZAEB=ZAEF,:.ZAED=ZAEF+ZDEF=ZcEF+ZBEF=(ZcEF+ZBEF)=90°oAAE±DEঝAC¨2DGDPJ_AB2P,••ᵫজ#$B,FᐵAE¾Þ$B=F,.\B+N=F+N,ßF,,N(2ᐳ0ÈFN_LABá$ᨵᨬ³$VDP1AB,AD=AB+cD=6,AZDPB=ZABc=Zc=90°,$h4)DPBc,¡)$ABP=Dc=2,AP=AB-BP=2,ᙠRtZkAPDl$DP==,VFN±AB,ᵫজ#AF=AB=4,$FN஻DP,AAAFN^AADP

36••$ᓽ$AFN=,AB+NḄᨬ³MூA᪆௃ூᑖ᪆௃1᪷&.ᑖḄå^ᓽTbH.2জᙠAD1´K2FÙDF=Dc,efEF.ᑖ0+NFDE=ZcDE᪷&ᐰ()ᑨ+SAS½FEDgZicDE,ᵫᐰ()ឋn⊡+NDFE=ZDcE=ZAFE=90°,ZDEF=ZDEcᵫ7()ᐰḄᑨ+HLRtAAFE^RtAABE,ᵫᐰ()ឋnNAEBZNAEF,ᵫ⊡+AE_LDE.ঝ¨2DGDP_LAB2Pᵫজ#$B,FᐵAE¾Þ$᪷&¾Þឋn#B=F,ßF,,N(2ᐳ0ÈFN±ABá$ᨵᨬ³$ᓽB+N=F+N=FNᙠRtZkAPDl$᪷&tu+ᳮDP==ᵫ¼()ᑨ+½AFN^AADP,ᵫ¼()ឋn$ëwFN,ᓽB+NḄᨬ³.

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