直角三角形ABC，角A=90度，AD垂直BC，BE平分角ABC分别交AD和AC于M、E，EN平分角BEC交BC于N，求证AMNE,

证明:作MX垂直与AB交AB于点X 可知：三角形DMB和三角形BXM全等。则DB=BX DM=MX ∠DMB=∠BMX 在三角形DBA中 ∠DAB+∠ABC=90°在三角形AXM中 ∠DAB+∠AMX=90°所以∠ABC=∠AXM 而在四边形BDMX中∠ABC+∠DMX=180°故∠AXM+∠DMX=180°从而N M X共线。在三角形DNM和XMA中∠DMN=∠BMX ∠NDM=∠MXA=90° DM=MX 所以三角形NDM全等于三角形XMA所以ND=XA NM=MA 所以DB+ND=BX+XA 即BN=AB 加之∠CBE=∠EBA BE公用 所以三角形BNE和BEA全等所以 ∠BNE=∠BAC=90°而∠BDA=90度 所以NE平行与AD ∠DAB+∠DAC=90°∠BNM=∠DAB（三角形NED全等于三角形XMA）所以∠BNM+∠DAC=90°而∠BNM+DMN=90° 故∠DMN=∠DAB所以 NM平行于CA 所以四边形AMNE为平行四边形 ，加之MN=MA(已经证明）故而 AMNE为菱形。

∵点E是CD中点

∴CE=1/2CD=1

勾股定理得BE=根号（BC�0�5+CE�0�5）=根号5

设NE=BN=x，则CN=2-x

∴（2-x）�0�5 +1�0�5=x�0�5

解得：x=5/4 2-x=3/4 即BN=5/4，CN=3/4

设ME与AD交于G

由于∠NEF=90°，∠C=∠D，

∴∠GED+∠NEC=90°，∠GED+∠DGE=90°，

∴∠NEC=∠DGE

且CE=CD

∴△NEC≌△EDG

∴GD=CN=3/4，AG=AD-GD=5/4，GE=NE=5/4

∴GF=FE-GE=3/4

设AM=MF=x，则MG=5/4-x

（5/4-x）�0�5=（3/4）�0�5 + x�0�5

解得：x=2/5 即AM=2/5

大概就是这个，MN的我不会求。

Many students thinks that study that the foreign language is very difficultBut as long as we work hard to study, can obtain the score

First, to become a good language learner, we should should be very clear to the understanding of the phrasingThe next in order, the distich son should acquaint withTo the single phrase too is

AAA,BAA,CAA,DAA,EAA,FAA,GAA,HAA,IAA,JAA,KAA,LAA,MAA,NAA,OAA,PAA,QAA,RAA,SAA,TAA,UAA,VAA,WAA,XAA,YAA,ZAA,

ABA,BBA,CBA,DBA,EBA,FBA,GBA,HBA,IBA,JBA,KBA,LBA,MBA,NBA,OBA,PBA,QBA,RBA,SBA,TBA,UBA,VBA,WBA,XBA,YBA,ZBA,

ACA,BCA,CCA,DCA,ECA,FCA,GCA,HCA,ICA,JCA,KCA,LCA,MCA,NCA,OCA,PCA,QCA,RCA,SCA,TCA,UCA,VCA,WCA,XCA,YCA,ZCA,

ADA,BDA,CDA,DDA,EDA,FDA,GDA,HDA,IDA,JDA,KDA,LDA,MDA,NDA,ODA,PDA,QDA,RDA,SDA,TDA,UDA,VDA,WDA,XDA,YDA,ZDA,

AEA,BEA,CEA,DEA,EEA,FEA,GEA,HEA,IEA,JEA,KEA,LEA,MEA,NEA,OEA,PEA,QEA,REA,SEA,TEA,UEA,VEA,WEA,XEA,YEA,ZEA,

AFA,BFA,CFA,DFA,EFA,FFA,GFA,HFA,IFA,JFA,KFA,LFA,MFA,NFA,OFA,PFA,QFA,RFA,SFA,TFA,UFA,VFA,WFA,XFA,YFA,ZFA,

AGA,BGA,CGA,DGA,EGA,FGA,GGA,HGA,IGA,JGA,KGA,LGA,MGA,NGA,OGA,PGA,QGA,RGA,SGA,TGA,UGA,VGA,WGA,XGA,YGA,ZGA,

AHA,BHA,CHA,DHA,EHA,FHA,GHA,HHA,IHA,JHA,KHA,LHA,MHA,NHA,OHA,PHA,QHA,RHA,SHA,THA,UHA,VHA,WHA,XHA,YHA,ZHA,

AIA,BIA,CIA,DIA,EIA,FIA,GIA,HIA,IIA,JIA,KIA,LIA,MIA,NIA,OIA,PIA,QIA,RIA,SIA,TIA,UIA,VIA,WIA,XIA,YIA,ZIA,

AJA,BJA,CJA,DJA,EJA,FJA,GJA,HJA,IJA,JJA,KJA,LJA,MJA,NJA,OJA,PJA,QJA,RJA,SJA,TJA,UJA,VJA,WJA,XJA,YJA,ZJA,

AKA,BKA,CKA,DKA,EKA,FKA,GKA,HKA,IKA,JKA,KKA,LKA,MKA,NKA,OKA,PKA,QKA,RKA,SKA,TKA,UKA,VKA,WKA,XKA,YKA,ZKA,

ALA,BLA,CLA,DLA,ELA,FLA,GLA,HLA,ILA,JLA,KLA,LLA,MLA,NLA,OLA,PLA,QLA,RLA,SLA,TLA,ULA,VLA,WLA,XLA,YLA,ZLA,

AMA,BMA,CMA,DMA,EMA,FMA,GMA,HMA,IMA,JMA,KMA,LMA,MMA,NMA,OMA,PMA,QMA,RMA,SMA,TMA,UMA,VMA,WMA,XMA,YMA,ZMA,

ANA,BNA,CNA,DNA,ENA,FNA,GNA,HNA,INA,JNA,KNA,LNA,MNA,NNA,ONA,PNA,QNA,RNA,SNA,TNA,UNA,VNA,WNA,XNA,YNA,ZNA,

AOA,BOA,COA,DOA,EOA,FOA,GOA,HOA,IOA,JOA,KOA,LOA,MOA,NOA,OOA,POA,QOA,ROA,SOA,TOA,UOA,VOA,WOA,XOA,YOA,ZOA,

APA,BPA,CPA,DPA,EPA,FPA,GPA,HPA,IPA,JPA,KPA,LPA,MPA,NPA,OPA,PPA,QPA,RPA,SPA,TPA,UPA,VPA,WPA,XPA,YPA,ZPA,

AQA,BQA,CQA,DQA,EQA,FQA,GQA,HQA,IQA,JQA,KQA,LQA,MQA,NQA,OQA,PQA,QQA,RQA,SQA,TQA,UQA,VQA,WQA,XQA,YQA,ZQA,

ARA,BRA,CRA,DRA,ERA,FRA,GRA,HRA,IRA,JRA,KRA,LRA,MRA,NRA,ORA,PRA,QRA,RRA,SRA,TRA,URA,VRA,WRA,XRA,YRA,ZRA,

ASA,BSA,CSA,DSA,ESA,FSA,GSA,HSA,ISA,JSA,KSA,LSA,MSA,NSA,OSA,PSA,QSA,RSA,SSA,TSA,USA,VSA,WSA,XSA,YSA,ZSA,

ATA,BTA,CTA,DTA,ETA,FTA,GTA,HTA,ITA,JTA,KTA,LTA,MTA,NTA,OTA,PTA,QTA,RTA,STA,TTA,UTA,VTA,WTA,IGB,JGB,KGB,LGB,MGB,NGB,OGB,PGB,QGB,RGB,SGB,TGB,UGB,VGB,WGB,XGB,YGB,ZGB,

AHB,BHB,CHB,DHB,EHB,FHB,GHB,HHB,IHB,JHB,KHB,LHB,MHB,NHB,OHB,PHB,QHB,RHB,SHB,THB,UHB,VHB,WHB,XHB,YHB,ZHB,

AIB,BIB,CIB,DIB,EIB,FIB,GIB,HIB,IIB,JIB,KIB,LIB,MIB,NIB,OIB,PIB,QIB,RIB,SIB,TIB,UIB,VIB,WIB,XIB,YIB,ZIB,

AJB,BJB,CJB,DJB,EJB,FJB,GJB,HJB,IJB,JJB,KJB,LJB,MJB,NJB,OJB,PJB,QJB,RJB,SJB,TJB,UJB,VJB,WJB,XJB,YJB,ZJB,

AKB,BKB,CKB,DKB,EKB,FKB,GKB,HKB,IKB,JKB,KKB,LKB,MKB,NKB,OKB,PKB,QKB,RKB,SKB,TKB,UKB,VKB,WKB,XKB,YKB,ZKB,

ALB,BLB,CLB,DLB,ELB,FLB,GLB,HLB,ILB,JLB,KLB,LLB,MLB,NLB,OLB,PLB,QLB,RLB,SLB,TLB,ULB,VLB,WLB,XLB,YLB,ZLB,

AMB,BMB,CMB,DMB,EMB,FMB,GMB,HMB,IMB,JMB,KMB,LMB,MMB,NMB,OMB,PMB,QMB,RMB,SMB,TMB,UMB,VMB,WMB,XMB,YMB,ZMB,

ANB,BNB,CNB,DNB,ENB,FNB,GNB,HNB,INB,JNB,KNB,LNB,MNB,NNB,ONB,PNB,QNB,RNB,SNB,TNB,UNB,VNB,WNB,XNB,YNB,ZNB,

AOB,BOB,COB,DOB,EOB,FOB,GOB,HOB,IOB,JOB,KOB,LOB,MOB,NOB,OOB,POB,QOB,ROB,SOB,TOB,UOB,VOB,WOB,XOB,YOB,ZOB,

APB,BPB,CPB,DPB,EPB,FPB,GPB,HPB,IPB,JPB,KPB,LPB,MPB,NPB,OPB,PPB,QPB,RPB,SPB,TPB,UPB,VPB,WPB,XPB,YPB,ZPB,

AQB,BQB,CQB,DQB,EQB,FQB,GQB,HQB,IQB,JQB,KQB,LQB,MQB,NQB,OQB,PQB,QQB,RQB,SQB,TQB,UQB,VQB,WQB,XQB,YQB,ZQB,

ARB,BRB,CRB,DRB,ERB,FRB,GRB,HRB,IRB,JRB,KRB,LRB,MRB,NRB,ORB,PRB,QRB,RRB,SRB,TRB,URB,VRB,WRB,XRB,YRB,ZRB,

ASB,BSB,CSB,DSB,ESB,FSB,GSB,HSB,ISB,JSB,KSB,LSB,MSB,NSB,OSB,PSB,QSB,RSB,SSB,TSB,USB,VSB,WSB,XSB,YSB,ZSB,

ATB,BTB,CTB,DTB,ETB,FTB,GTB,HTB,ITB,JTB,KTB,LTB,MTB,NTB,OTB,PTB,QTB,RTB,STB,TTB,UTB,VTB,WTB,XTB,YTB,ZTB,

AUB,BUB,CUB,DUB,EUB,FUB,GUB,HUB,IUB,JUB,KUB,LUB,MUB,NUB,OUB,PUB,QUB,RUB,SUB,TUB,UUB,VUB,WUB,XUB,YUB,ZUB,

AVB,BVB,CVB,DVB,EVB,FVB,GVB,HVB,IVB,JVB,KVB,LVB,MVB,NVB,OVB,PVB,QVB,RVB,SVB,TVB,UVB,VVB,WVB,XVB,YVB,ZVB,

AWB,BWB,CWB,DWB,EWB,FWB,GWB,HWB,IWB,JWB,KWB,LWB,MWB,NWB,OWB,PWB,QWB,RWB,SWB,TWB,UWB,VWB,WWB,XWB,YWB,ZWB,

AXB,BXB,CXB,DXB,EXB,FXB,GXB,HXB,IXB,JXB,KXB,LXB,MXB,NXB,OXB,PXB,QXB,RXB,SXB,TXB,UXB,VXB,WXB,XXB,YXB,ZXB,

AYB,BYB,CYB,DYB,EYB,FYB,GYB,HYB,IYB,JYB,KYB,LYB,MYB,NYB,OYB,PYB,QYB,RYB,SYB,TYB,UYB,VYB,WYB,XYB,YYB,ZYB,

AZB,BZB,CZB,DZB,EZB,FZB,GZB,HZB,IZB,JZB,KZB,LZB,MZB,NZB,OZB,PZB,QZB,RZB,SZB,TZB,UZB,VZB,WZB,XZB,YZB,ZZB,

AAC,BAC,CAC,DAC,EAC,FAC,GAC,HAC,IAC,JAC,KAC,LAC,MAC,NAC,OAC,PAC,QAC,RAC,SAC,TAC,UAC,VAC,WAC,XAC,YAC,ZAC,

ABC,BBC,CBC,DBC,EBC,FBC,GBC,HBC,IBC,JBC,KBC,LBC,MBC,NBC,OBC,PBC,QBC,RBC,SBC,TBC,UBC,VBC,WBC,XBC,YBC,ZBC,

ACC,BCC,CCC,DCC,ECC,FCC,GCC,HCC,ICC,JCC,KCC,LCC,MCC,NCC,OCC,PCC,QCC,RCC,SCC,TCC,UCC,VCC,WCC,XCC,YCC,ZCC,

ADC,BDC,CDC,DDC,EDC,FDC,GDC,HDC,IDC,JDC,KDC,LDC,MDC,NDC,ODC,PDC,QDC,RDC,SDC,TDC,UDC,VDC,WDC,XDC,YDC,ZDC,

AEC,BEC,CEC,DEC,EEC,FEC,GEC,HEC,IEC,JEC,KEC,LEC,MEC,NEC,OEC,PEC,QEC,REC,SEC,TEC,UEC,VEC,WEC,XEC,YEC,ZEC,

AFC,BFC,CFC,DFC,EFC,FFC,GFC,HFC,IFC,JFC,KFC,LFC,MFC,NFC,OFC,PFC,QFC,RFC,SFC,TFC,UFC,VFC,WFC,XFC,YFC,ZFC,

AGC,BGC,CGC,DGC,EGC,FGC,GGC,HGC,IGC,JGC,KGC,LGC,MGC,NGC,OGC,PGC,QGC,RGC,SGC,TGC,UGC,VGC,WGC,XGC,YGC,ZGC,

AHC,BHC,CHC,DHC,EHC,FHC,GHC,HHC,IHC,JHC,KHC,LHC,MHC,NHC,OHC,PHC,QHC,RHC,SHC,THC,UHC,VHC,WHC,XHC,YHC,ZHC,

AIC,BIC,CIC,DIC,EIC,FIC,GIC,HIC,IIC,JIC,KIC,LIC,MIC,NIC,OIC,PIC,QIC,RIC,SIC,TIC,UIC,VIC,WIC,XIC,YIC,ZIC,

AJC,BJC,CJC,DJC,EJC,FJC,GJC,HJC,IJC,JJC,KJC,LJC,MJC,NJC,OJC,PJC,QJC,RJC,SJC,TJC,UJC,VJC,WJC,XJC,YJC,ZJC,

AKC,BKC,CKC,DKC,EKC,FKC,GKC,HKC,IKC,JKC,KKC,LKC,MKC,NKC,OKC,PKC,QKC,RKC,SKC,TKC,UKC,VKC,WKC,XKC,YKC,ZKC,

ALC,BLC,CLC,DLC,ELC,FLC,GLC,HLC,ILC,JLC,KLC,LLC,MLC,NLC,OLC,PLC,QLC,RLC,SLC,TLC,ULC,VLC,WLC,XLC,YLC,ZLC,

AMC,BMC,CMC,DMC,EMC,FMC,GMC,HMC,IMC,JMC,KMC,LMC,MMC,NMC,OMC,PMC,QMC,RMC,SMC,TMC,UMC,VMC,WMC,XMC,YMC,ZMC,

ANC,BNC,CNC,DNC,ENC,FNC,GNC,HNC,INC,JNC,KNC,LNC,MNC,NNC,ONC,PNC,QNC,RNC,SNC,TNC,UNC,VNC,WNC,XNC,YNC,ZNC,

AOC,BOC,COC,DOC,EOC,FOC,GOC,HOC,IOC,JOC,KOC,LOC,MOC,NOC,OOC,POC,QOC,ROC,SOC,TOC,UOC,VOC,WOC,XOC,YOC,ZOC,

APC,BPC,CPC,DPC,EPC,FPC,GPC,HPC,IPC,JPC,KPC,LPC,MPC,NPC,OPC,PPC,QPC,RPC,SPC,TPC,UPC,VPC,WPC,XPC,YPC,ZPC,

AQC,BQC,CQC,DQC,EQC,FQC,GQC,HQC,IQC,JQC,KQC,LQC,MQC,NQC,OQC,PQC,QQC,RQC,SQC,TQC,UQC,VQC,WQC,XQC,YQC,ZQC,

ARC,BRC,CRC,DRC,ERC,FRC,GRC,HRC,IRC,JRC,KRC,LRC,MRC,NRC,ORC,PRC,QRC,RRC,SRC,TRC,URC,VRC,WRC,XRC,YRC,ZRC,

ASC,BSC,CSC,DSC,ESC,FSC,GSC,HSC,ISC,JSC,KSC,LSC,MSC,NSC,OSC,PSC,QSC,RSC,SSC,TSC,USC,VSC,WSC,XSC,YSC,ZSC,

ATC,BTC,CTC,DTC,ETC,FTC,GTC,HTC,ITC,JTC,KTC,LTC,MTC,NTC,OTC,PTC,QTC,RTC,STC,TTC,UTC,VTC,WTC,XTC,YTC,ZTC,

AUC,BUC,CUC,DUC,EUC,FUC,GUC,HUC,IUC,JUC,KUC,LUC,MUC,NUC,OUC,PUC,QUC,RUC,SUC,TUC,UUC,VUC,WUC,XUC,YUC,ZUC,

AVC,BVC,CVC,DVC,EVC,FVC,GVC,HVC,IVC,JVC,KVC,LVC,MVC,NVC,OVC,PVC,QVC,RVC,SVC,TVC,UVC,VVC,WVC,XVC,YVC,ZVC,

AWC,BWC,CWC,DWC,EWC,FWC,GWC,HWC,IWC,JWC,KWC,LWC,MWC,NWC,OWC,PWC,QWC,RWC,SWC,TWC,UWC,VWC,WWC,XWC,YWC,ZWC,

AXC,BXC,CXC,DXC,EXC,FXC,GXC,HXC,IXC,JXC,KXC,LXC,MXC,NXC,OXC,PXC,QXC,RXC,SXC,TXC,UXC,VXC,WXC,XXC,YXC,ZXC,

AYC,BYC,CYC,DYC,EYC,FYC,GYC,HYC,IYC,JYC,KYC,LYC,MYC,NYC,OYC,PYC,QYC,RYC,SYC,TYC,UYC,VYC,WYC,XYC,YYC,ZYC,

AZC,BZC,CZC,DZC,EZC,FZC,GZC,HZC,IZC,JZC,KZC,LZC,MZC,NZC,OZC,PZC,QZC,RZC,SZC,TZC,UZC,VZC,WZC,XZC,YZC,ZZC,

AAD,BAD,CAD,DAD,EAD,FAD,GAD,HAD,IAD,JAD,KAD,LAD,MAD,NAD,OAD,PAD,QAD,RAD,SAD,TAD,UAD,VAD,WAD,XAD,YAD,ZAD,

ABD,BBD,CBD,DBD,EBD,FBD,GBD,HBD,IBD,JBD,KBD,LBD,MBD,NBD,OBD,PBD,QBD,RBD,SBD,TBD,UBD,VBD,WBD,XBD,YBD,ZBD,

ACD,BCD,CCD,DCD,ECD,FCD,GCD,HCD,ICD,JCD,KCD,LCD,MCD,NCD,OCD,PCD,QCD,RCD,SCD,TCD,UCD,VCD,WCD,XCD,,GSW,HSW,ISW,JSW,KSW,LSW,MSW,NSW,OSW,PSW,QSW,RSW,SSW,TSW,USW,VSW,WSW,XSW,YSW,ZSW,

AIX,BIX,CIX,DIX,EIX,FIX,GIX,HIX,IIX

证明：

因为AD、BE分别是等边△ABC中BC、AC上的高，

所以∠BDM=∠CEN=90°

所以∠DBM+∠M=90°，∠ACN+∠N=90°

又因为∠CBM=∠ACN

所以∠M=∠N,

因为在等边三角形ABC中，∠ABC=∠ACB,

所以∠ABC+∠CBM=∠ACB+∠ACN

即∠ABM=∠BCN

在△ABM和△BCN中，

∠M=∠N,

∠ABM=∠BCN

AB=BC

所以△≌△(AAS)

所以AM=BN

在BC上截取BM＝BA，BN＝BE，

∵BE平分∠ABC，

∴∠ABE＝∠CBE＝20度，

又∵BA＝BM，

BE＝BE，

∴△ABE≌△MBE（SAS）

∴AE＝ME，

∠BME＝∠A＝100度，

∴∠EMN＝180-∠BME＝180-100＝80度

又∵∠A＝100度，AB＝AC，

∴∠ABC＝∠C＝40度，

在△BNE中，

∵∠CBE＝20度，BN＝BE，

∴∠BEN＝∠BNE＝80度＝∠EMN，

∴EM＝EN，

∴∠ENC＝180-∠BNE＝180-100＝80度

∴∠NEC＝180-∠ENC-∠C＝180-100-40＝40度＝∠C，

∴EN＝NC，

∴等量代换可得：NC＝EN＝EM＝AE，

∴BC＝BN+NC＝BE+AE．

求采纳为满意回答。