正方形ABCD中,BD⊥CE^BD=CE平移后也成立2.C D6.邊△=BE=CDΔABD,ΔACE為等BE、CD相交所成銳角為60°ABDE與ACFG為正方形=EC=BG,BG⊥CE注：條件可換成?BAE,?CAG為等腰Rt?7.8.①AD平分NCAB；②DE△ABC為等腰Rt?,AE平分∠CAB,∠DAE=2BD90°n5.ΔACD??BCE為等邊△,A、C、B共線(xiàn)=AC=BC,則CE ?ACE也?DCB;?ACM也?DCN?MCE也?NCB;AE=BD,AM=DN,EM=BN,CM=CN,AE、LBDOCE=BD BD相交成銳角60。，=C0,C)C平分NAe)B,有些變化.10.4 AC=BC 15.AMDEF為等腰Zλy~f__-BRt? AnPB+PC=2PD 16. C∕i?ZABP+ZC =A———L——?D180°AB=AC 17.anAE+BE=BC fAC=BC 18aγ---I——IOCF+DF=AD Bl-^c爪 =CD=CE=BGCefd為菱形工 rl F '工a MF bAB=ACnDE+DF=BM(鈍角△也成立)等腰梯形nEF+EG=CM7.19. ,? BF=AD=BFLAD聲-" ∕(RB cD J L\A DBA0=D0+C0,BO=EO+CO,OM+ON注：ABCE繞C旋轉(zhuǎn)時(shí)，結(jié)論=OD=OEBE+CD=BCAD=CDBOCD=BDoAD=BDnNA=NB或NA+NB=180°nDE+BF=EFAE平分NDEF,AF平分NBFEZ2=2Z1nAF=BC+CFnAE+CF=CDEF=拒OES —la2四邊形OEBF 4nBE+DF=AE=Nl=NB?ADC^ΔCDB^ΔACBAC2=AD?ABBC2=BD?BA25.BF=ACoBF⊥ACC中點(diǎn)四邊形EFGH至少是.：，取決于AC、BD的關(guān)系，EF，EH的關(guān)系對(duì)應(yīng)AC、BD的關(guān)系梯形ABCD中：①AE=BE;②AD+BC=CD;③DE⊥CE,知二推2D.AC?BC=AB?CDCD2=AD?BDZC=ZD0ΔABCsΔADE0AB?AD=AC?AEZB=ZE0ΔADEsΔACB0AD?AB=AC?AEnDF=EF d28.nAM2+BN2=MN2AD=BC=a,BF=CFnEF12nHF+HD=a∠1=∠C0ΔADE^ΔACBOAD?ABAE?AC∠1=∠Bo△ADC^^ACBO∠ADC=∠ACBoAC2=AD?AB31.nAO=2DODE0BO=2EOCO=2FO，PN0AD=BDAC=BC共斜邊的兩直角三角形，四個(gè)頂點(diǎn)在同一圓上。①△任意兩邊之積等于第三邊上的高與其外接圓直徑之積。如：AB?AC=AD?2R（鈍角△也適用）；②正弦定理： BC=2R（不能直接用，可構(gòu)Sin/BAC造以直徑為斜邊的Rt△，利用三角函數(shù)求。）FM的延長(zhǎng)線(xiàn)平分ACnAM=CM=FMAC=ECnBD=CD△ABE^^ADC^^CDE△ABDs^AECs^BED BD2=CD2=DE?DAAB?AC=AE?ADAE?DE=BE?CD若I為AABC內(nèi)心，則BT=CD=ID，關(guān)注∠BAC為特殊角時(shí)圖形的特殊性、及相關(guān)比值。nHD=FDCH⊥ABH點(diǎn)關(guān)于AC的對(duì)稱(chēng)點(diǎn)在圓上，H點(diǎn)關(guān)于AB的對(duì)稱(chēng)點(diǎn)在ab上，BD=CDoAD平分ACAE①AD⊥CD;②AC平分ADAB；③DC切。O于C中，知二推一。?PDM^?PNOCA平分NPCD?ONDs?θPNnr=-b-（注AC與BC不一定相等）a+bn①BO±OA；②RQ切。O于Q。③RP=RQ中，知二推一nOR可上、下平移，Q也可在AB上18 nAB+CD=AD+BC192021nBE=BD ?PBD^?PCE ?PBE^?PAD?PBAs?PCB BE?BD=AD?CE若AC是直徑，則?ADP=45°*若?BDE為等腰Rt?或等邊△時(shí)，上述結(jié)論有些變化。nAC=