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1、x二次根式xxx(7)(x,ax;.xxxxxxy;.bbbabcabc(b)beqoac(,20)ABCabcabbbABCcxyx(xxxx2;3);b;b(;.bbabababababbxyxyxxxx;,babababababbb;bb;bbxyxy2,,與,與bbbabbb(.(bbbbbbbb.xxnnabamnmnmmnbbbbb(.ababab*babbbbbbbb().bb.xxyyxyxymna;a;axxxxxxxx;abccxy6;b.;b;2;.;2;2;b;b.7;.aa3;(2).b.,nn(2;.mnmmnPmn:a,(xxabbababbbB已知AByxABB
2、,bbbbbbbbbbbaABCDADBC,Aeqoac(,90),BCDADABCD;nn用.b.x;nnnnnnn.勾股定理abccABCCabcABCabccabAacbAabcABCeqoac(,Rt)ABCBCABACBCABCABACBDACDCBDeqoac(,Rt)ABCCABADECBCFGeqoac(,Rt)ABCCABCabcabcabacbABCcabacAcchabcabcxxlABCDBAClSSSSSSSSABCCABDABCADBCeqoac(,14)ABCCSSSSSSSSSBABADAABACAABABCDABACBDCDCDABCDOW在ABC中,若ABA
3、CBC,則ABABCE在ABC中,若ABACBC,則BCADACBE在ABC中,若ACBC,ACBAB,則ACABCDABCABBCCAeqoac(,a)ABC在ABCACBACBCABCD,則ACABBCAEeqoac(,Rt)ABCCDEBCACADBEABeqoac(,10)ABCAACABABDCDDBACABBDABCDEFDBABADBEADDBCFABBCECeqoac(,13)ABCCDABEFACBCDEDFAEBFEFeqoac(,14)ABCABCABBClllllllACABCDACACEFAEAEGHABCDSSSSnnSnSnabcabcABCabcABCabcca
4、bccabccABCbabacBeqoac(,1)ABCaaaaaABCabcabccabcb,bbnnmmneqoac(,12)ABCDBCABADACBDCDABCDABBCABBCCDADABCDABCDFDCECBCEAFFECBBMPeqoac(,16)ABCabcabcABCabcABCacbcabnababacSSSSSSSSSACDAABCDO.BDDCmCEEAkkmkmABm,BDBDxCDxeqoac(,Rt)ACDxxxBEBExDEBExAEADDExABEABAEBExxxECECxDEEFxAFADBFCFeqoac(,Rt)xxxFDMDMDFAMEMAClMN
5、AMBBNCaacCDAEaAFEFAEAFEFAEabcababcnnnnnBCAABCACBBCABCABCCOABCODBCOEACOFABDEFBCCAOABACBCABBCABACADBDABCABACABCDBCABACBCADeqoac(,2)ABCabcaaaaaABCDABBCABCCDABEADEABCDBEeqoac(,Rt)ABCCCDABDABCD,則ACBCeqoac(,13)ABCCABABACADBCDADABCDABDABCDeqoac(,15)ABCABACPBCAPPBPCPeqoac(,16)ABCABACBCADBCABAnB、圖BACEBDxDEBD
6、xAEABCECDxeqoac(,Rt)CDEADEDEADeqoac(,BE)ABEeqoac(,Rt)CEABECEBE7,ADBCADEAAHBCHAPPBPCAHPHBHPHCHPHAHPHBHPHAHBHAB.eqoac(,Rt)ABCACBACBCABACDABDABADCDCBABDABBDCDABDABADBDxCDxxABD平行四行形ABCDeqoac(,在)ABCDABABeqoac(,若)ABCDACDABACBDABCDCEABEABCEABCDDBDCACEBDEBCEABCDAABADeqoac(,S)ABCDABCDAEABCDAEBADFAFEFABEFAEAF
7、AFBEABCDABCCADBCADBCAADCABCDABCDDEACEBFACFDEBFABCDABCCDEADEABFAFCEEFABCDABCDDEFBDECBGCBBGABCDEFACAECFBEDFBEDFABCDABADDABAABxBCDABCDABCDABCDEFABCDACBDOACBDABABCDAEAFBCCDEFEAFABAD,則CDABCDADBC;Deqoac(,)ABCDOAOBBOCABBCeqoac(,在)ABCDACBDOOAxACxOCeqoac(,在)ABCDCAABBADBCACABeqoac(,在)ABCDAEBCE,若ABBCBE,則ABCDAB
8、Ceqoac(,在)ABCDAAAACCCCABCDBBDDBCDAABCDeqoac(,,則)ABCDnnnnnnnABCDDABEEABABCDABDABBCABCDCEABECFADFOeqoac(,為)ABCDACOABCDOMNEFMNOEOFMAENCFABCDEACAEECFABBFeqoac(,AF)BEFeqoac(,,求)ABCDABCDABCDabcdabcdacbdABCDACBDACBDOBOCOAODOABCDABCDACBDOABCDABCDBCADABCDBADBCDABCDOAOCABCDDBACABABCDABCDEFABCDAECFMNDEFBENFMAB
9、CDEFADBCAECFAFBEGCEDFHEGFHABCDEFBADCAECFPQDEFBEQFPABCDEFDABCAECFFABERECDFSRESFABCDABDCADBCEBCFADAFCEEFBDOOBDeqoac(,14)ABCDACEBCABEEDFAECFCFAEeqoac(,15)ABCDABEACEFABDFBEDFAEABCABCABCDCEDFABEFABCDEFABGHADMNADAEFDEBCFABCDABCDADBCABCDABCDABBCADDCABCDCDABABCDABCDEFABCDABCDABCDADxACABCDACBDeqoac(,O)AODBEC
10、OAABCDEFACAECFFeqoac(,13)ABCEFABCDBCBCADEFOEFDFAEDFeqoac(,14)ABCABACDBCDFABACFDEACABEDEDFeqoac(,15)ABCDFCBBACDBFADADEACDCBFCDEFyxAABAOBPPAmmBmmmkMxNyABMNMNeqoac(,在)ABCDBCABEBCAEDeqoac(,在)ABCDxeqoac(,)ABCDACBDOABACABCeqoac(,60)OABM如圖,在ABCDBCAMBDADeqoac(,,則)ABCDMeqoac(,)ABCDACBDOBOCADBDeqoac(,,則)ABCDA
11、BCDABAD,BADBCE,交DCFBGAEGAFCEFBDABCDMNADABMNBDeqoac(,S)DMCeqoac(,S)BNCeqoac(,10)EFCAEFABECADFCEADFABABaADbEFCECFCeqoac(,11)ABCABCBDACDAEBACEFDCBCFBEFCABCDEADCEBAFBCCDFBCFABCDAEFABCDABADBFBDMPQPAxQByABQMOMOeqoac(,Q)OBQOAPQOPOQOPCQOPCQABCEFGABACBCABCEFEGGFeqoac(,A)BCABCEFGeqoac(,A)BCnDEABCABACDEADAE,則A
12、BCDEABCDEFGHABBCCDDAEFGHABCBDCEOFGOBOCDEFGEeqoac(,為)ABCDDCCEDCAEBCBDFGACBDOOFABOFABCDECDFAEFCBEGGFGCABCDADBCEFDCABFEADBCHGAHFBGFABCDBCAEBACBEAEEABACEDeqoac(,10)ABCDEABACBDCEMNBECDMNABPACQAPAQABCDACBDOAOBACABBCABCCACBCABCDABCDADABDDEAABCAEABABCDABBCACADBCEFCECEACABCDABCDACBDOOABOBAABCDBEACECFBDFBECFe
13、qoac(,11)ABCDBCEADABCBEFAFDCCFDBCABACADCFABCDABBCBDEFABCDEFBCABEFEDEFEDAEBADABCDABADCDEEBAECPBCBPCPEPABFABBFPAEPFBPABCDEFABACEFABCDABCDABABCDEABDEABABABCABCDABCDABCEABPACPBPEABABCDEFABCDDEBFBDADECBFADBDBFDEABCDABCDACBADCEADABEAECDEABABCABCDABACABBCACBDOACOBCADEFABEFAFECBEDFACOABCDBDEFADCDAECFBDEBCFB
14、EFBEFSSABCDBADBCDADABCD,使B;作ADBCD,以ADABCDBnABnCnDnADnaACEFABCDACEFABCDABCDBCECEACAECDFAFCBCACEEGABCDBCEFACEGBDF,如果EGEFEGABCDADCEDEPQPQABCDABCDEMNABBCADCEMNMCEANMEABCDACAEABEFACBCFBFECABCDCEFCGEFADHDHPABCDPEABEPFBCFDPEFABCDPABABDPACQPABADQABQPABADQABCDPABBCCPADQABCDeqoac(,12)ADECBFeqoac(,13)ADFCBEAED
15、CFBGEBDEAeqoac(,15)ABECDFBCDFFHABADHDCGEFFGGHHEEFGHFFHABADHEEGADDCGEFFGGHHEEFGHADHDHCFCDGEFFGGHHEEFGH)acbdABQPQMMNPQDCNQMPNQMNPABACAOABBCADBDBCBCxAByAOMCONAOECOFAMECNFABCCDAOAOCOEeqoac(,OF)OAEOCFEAOFCOABCDABCDBAODCOEAMNCF,bd.ADBCBFDEEMNFAFCEBFDEGEFHGFEHEBFDEPQFEBFDREASFCRESFBFDEBEDFAFCEDFAEDEAFADEFB
16、FDFBFDEBEDFDFBFDEBFDBCDEDFABCACCBACDCBFCDeqoac(,BF)ACDCBFACDCBFADCFCADBCFAEDADEADDEFCDEEDBBDACADACDBCFEDBBCFEDFCEDFCCDEF(,PPmkx提示:作DEAMBCE,作DFBEeqoac(,F),可得BDEDFCEBDEOExBECEBCxeqoac(,S)eqoac(,S)BCDBDCEBMDNEFECFCabEEMBCDCeqoac(,M)AEBAEMDCAFeqoac(,DE)ADEADBABDykxMQMOQm)SOBQOBBQOBBQmmmSmOAPmQQQOPCQOPCQ
17、OQPCP,OPOPCQOQQQQnOQnnnnOQOQOQOQOQOPOPCQOPOQnBDACBECEABABECBFFCABCDAOOCABOFBEPEFPCACACMMEMFEMFMEDBEACFAPAQBCHMHeqoac(,NH)MHNAPQAQPOAOBACBDBOECOFADCFeqoac(,13)BFECEDBEDCABBAEAEBADDCEAEBEAEABEBAECBEFBFEBEABABBEBFBFDEABCeqoac(,Rt)BEDFBEFBEF()n.aDDFNMBCFAFCHDHBPADQABQQAQEyEQFxFQADQESQEQACQ(,)D(,)y2xyxPA
18、BADQABCDADQQDQADADQAQADPBABCDQDQAADQPCQCDAeqoac(,DQ)ADQPBCCPxADAQADBCADQCPQAQDCQPADQAQDCQPCPQCQCPxACAQADxCQACAQCPADQeqoac(,在)ABCDABADAABCDABCDAECF若AB,則BCABCDEBCFBCABEFABCDACABCDABCDABCDEABBEAEPBDPEPAABCDOABAOABCOABCOOABAOABCOABCnOnABCDEFBCADAFCEAECFABCDBBCADEBECCFBEFBFBFABCDBDCEBEADFABFEDFFBCMDMBMDFABCDADBCEFGHDBBCACDAHFEGABCDADBCCECDFBCFAEDAEAEFABCDADBCCFBCPABABAPCBPDPCPAPDPBAPCBPDCDEFGHACABB
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