立体几何复习课件 江苏省扬中高级中学

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立体几何复习课件 江苏省扬中高级中学. 刘新春. 体积面积问题. 平行问题. 立几概念和方法. 垂直问题. 动态的立体几何. 角度问题. 正方体的截面问题. 距离问题. 三棱柱的体积分割. 柱锥问题. 多面体与球的问题. 综合问题. 生活问题和翻折问题. 返回. 平行问题. 返回. 例: 有以下四个命题: ① 若一条直线与另一条直线平行,则它就与经过另一条直线的平面平行; ② 若一条直线垂直于一个平面的一条垂线,则此直线平行于这个平面; - PowerPoint PPT Presentation

Transcript of 立体几何复习课件 江苏省扬中高级中学

  • ( A B C D D

  • 1AA

  • 2Al Al

  • 3

  • 4

  • 5l1 // l2 , l1 ,l2 l1 //

  • 6ab,ab a

  • L,L,( )A C B D

  • A C B D L,L,( )

  • L,L,( )A C B D D

  • A0 B1 C2 D3

  • A

  • (1)(2)

  • a b a//ba//ab(1) a,b=b(2) aaPP =b(3) a//b(4) a //

  • ,P-ABC,M,NPCAPBC,:MN//BCAPMN// EF MN //BCA

  • ,ABCDABEFAB,M.NAM=FN:MN//BCEABCDEFMNMN // GH MN //BCE

  • ABCDEFMNAFN BNH AN/NH=FN/BN AN/NH=AM/MC MN//CH MN //BCE,ABCDABEFAB, M.NAM=FN:MN//BCE

  • AC1EDD1DB1//A1C1EEDB1 // EF DB1 //A1C1E

  • AC1OADD1A1CO // A1C1BB1O

  • (1)(2)(3)

  • a//,a, =ba//b =bb a //a b=a//b

  • abc

  • ala // a// =la // l

  • abABOMNPa,bOABOa,bMNPMP=PN

  • 123

  • 42351

  • 123

  • 4.5.,a

  • 2. ,ABCD ABCDMP ABCD MP // .

  • :,ABCD-A1B1C1D1 AB1D1BDC1B1D1AB1=B1AB1D1BDC1

  • 2A1CBDBDBC1=BA1CBDC1AB1D1BDC1

  • 1:ABCD-A1B1C1D1E,F,GA1D1,A1B1,A1A,EFGBDC12:OBDOC1 EFG

    O EFGBDC1OC1 EFG

  • 3:,ABCD-A1B1C1D1 E,F,M,NA1B1,A1D1, B1C1, C1D1 AEFBDMN

  • A-BCDE,F,GAB,AC,AD.EFGBCD

  • (1)(2)1(3)2

  • (1)(2)

  • 1l , m l____m2 n, m , mn_____, l m, l n, l 3l , m , l____m4l //m , l , m____ //

  • PABCABOCABPAO1BCPAC

  • PABC2)AHPC,AHPBCABOCABPAO

  • OAC1,O,ACD1B1BD

  • OHAC1OB1H D1O,B1HD1AC

  • : l // ,m : l m m

  • CAB PAABCPAABCPACABCPABABCBCPACPBCPAC

  • l l

  • l l

  • ABCDADCBCDABD BCDDEBC ADE ABC ADCBCDABD BCDAD BCDAD BCDE BCBC ADEABC ADE

  • ABC, ACB=90,PPA=PB=PC . PAB ABC

  • ABCDAB=BCAD=CDEAC( (A) ABD BCD(B) BCD ABC(C) ACD ABC(D) ACD BDE

  • ABCDPA ABCDPB,PC,PD,AC,BD,PACABCDPABABCDPADABCDPADPABPADPCDPBCPABPBDPAC

  • P-ABCPBABCACB= 90,PB=BC=CA,EPC

  • P-ABCDPAABCDBAD= 120,EPC

  • :SABCASC=90ASB=BSC=60SA=SB=SCASCABC

  • aboaba//ab//babab

  • oabOooooo

  • aboaba//ab//babab

  • BA

  • aboaba//ab//babab

  • ABO

  • aboaba//ab//bababALBO

  • 2.3.b.a.c. 1.

  • AC1A1BB1CA1BB1C60A1B60

  • AC1D1BB1CABDCA1B1D1C1

  • AC1M,NA1AB1BCMD1NMN

  • PABCMNP-ABCMNPBACPA=BC=4MN=3PABC

  • 1. AC1EGAA1CC1 FABC1EEFEFGD (A) 30 (B) 45 (C) 60(D) 90DM EB1EC1AB1EB1 EFDGAMEB1EF DG

  • a,b50 PPa,b30 abPO2

  • A1ABB1CDC1D1FEABG O1:ABCD-A1B1C1D1EFBB1 CDAED1F

  • 2ABCD-A' B'C' D', AB=BC=4, AA' =6, EFBB' CC', AEBF.

  • 3ABCD-A1B1C1D1AB=AA1=2 cm AD=1cmA1C1BD1

  • BB1MO1MO1MD1BB1D1A1C1 O1A1O1MA1C1BD1O1M

  • A1C1EA1C1BD1 A1EC1EA1C1EA1C1BD1()BC1B1F

  • ABCDA1B1C1D1ACBC1 A30 B45 C60 D90

  • SA BCEFSC A BEFSA A90 B60 C45 D30

  • ACGEGFG EG//SA GEFEFSAFG//BCSABC EGF=90 EGFEG=SAFG=BC EG=FGEGF GEF=45C.

  • ABCD- A1B1C1D1,ACBDO,OB1A1C11900

  • S-ABCSABC, E, FSCAB EF SA CD(A)300 (B)450 (C)600 (D)9002B

  • : a , M AB , N BB1 A1M C1 N EGABE, BE, BE A1M CC1G,BG. BG C1N EBGBG=BE= a, F C1 = acosEBG=2/5FEB1FNF,BENFFNCEBG

  • 11 2 1 cos 0 2 cos 0 3 cos = 0 3 90o2

  • 0 ]

  • AB2AB 60

  • C

  • l160 9060Ol1

  • l130 l2 l1 60 , l2 ?l1

  • ,OA,OCOAOB,AOC2:cos2= cos 1 cos

  • ,:(1)(2),

  • :ABCD-A1B1C1D1A1BA1B1CDO

  • SACBOFEACB=90SABC SCA= SCB= 60SCACB.

  • SACBOFESA,SB,SCBSC=60,SAPBSC3, PSB,SC5,SABSCP

  • ABCDFEADFDACA1BEABCD3AE=2BECF=2DFEFAEFDAGBCAEABCD

  • ABCD-A1B1C1D1OACA1OBB1D1D.OO`

  • PABCPAABCPABCD

  • 1.abab.______________.

  • 2.ABCDA1B1C1D1B1-AA1-C1_____B-AA1-D______C1-BD-C_______.4590

  • 3. -l-AB l 4530 ________________.45135

  • B

  • 5. PAPBPCP60oB PAC ( )

    A. B. C. D.AD

  • ABCAMABCAMA ABCS ABCSA-BC-A.COS = S S

  • AC1D1-AC-D

  • ABCDASAABCDSBCSCDABCD45B-SC-D.E

  • 7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.

  • 7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.: (1)A1MABCA1M AA1C1C(1)AA1C1CABCBCACAA1C1CABC=ACBC AA1C1C

  • 7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.: (2)A1MABCAA1ABCA1AC,A1AC=60o,MACAA1C,CNAA1NNAA1,BNBC AA1C1CBCAA1AA1 BNCAA1 BN BNCB--AA1C

  • 7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.AC=BC=aAA1CaBNCBAA1C

  • AC1EFABADC1-EF-CEFABDCA1B1D1C1H

  • ABC,ABBC,SA ABC,DESC,SA=AB,SB=BC,E-BD-C?SABCED

  • E

  • P-ABCPA ABCPA=3AC=4PB=PC=BC. 1P-BC-A34H

  • 2A-PC-BCOS =P-ABCPA ABCPA=3AC=4PB=PC=BC. 1P-BC-A

  • AC1E,F,A1ECFABCD.EF

  • EFAC1E,F,A1ECFABCD.

  • ABC-A1B1C12, (1) AB1A1C?(2)AB1BB1C1C?(3) DCC1,AB1DABC?

    A1AB1C1BC

  • ABC-A1B1C12, (1) AB1A1C?

  • : A1A,AC, A1B1N,M, G,GN,NM.GNM.GM.GMGM=N

  • 1. ABC-A1B1C12, (1) AB1A1C?(2)AB1BB1C1C?E

  • ABC-A1B1C12,(3) DCC1,AB1DABC?A1AB1C1BCD

  • :AG

  • A1AB1C1BCDM B1ABB1AMB.

  • B1DBCM,AM

  • CABDA1B1C1D1MN

  • CABDA1B1C1D1MN

  • CABDA1B1C1D1MN

  • CABDA1B1C1D1MN

  • CABDA1B1C1D1MN

  • CABDA1B1C1D1MN

  • B1A1C1 ABC ABCA1 B1 C1 BAC=90AB=BB1=1B1CABC30 BB1C AB B1CAB1CB1C

  • C1 AA1B1BC

  • 1.(1)

    (2)2.(1).(2).

  • -AB-C

    (AB)DCE

    ABCEB( )

    (A)CEBDEB (B)CEB=DEB

    (C)CEBDEB

    (D)CEBDEBA

  • D

  • 112ABCDA1B1

    C1D1BA1C1ABCD__

    _____.arccos(1/3)

  • 5.ABCDACBDO

    ABCDBD604

    ACBDADCOAOC

    BlBCDlAOC,

    ________

  • 6. PABCPCABC AB=BC=CA=PCBAPC EFBBEACEEEFPAFBFPCABCBEPACBFPABFEBPACPC=1 AB=BC=CA=PC=1EAC

  • 7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.

  • 7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.: (1)D-AC-B,DCAC,DCABC,()AB ABC,DCAB,ABBC,ABBCDABCD

  • 7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.: (2)CCHDBH,ABDDCB,CHABD,ABBCDABD DCB=DB,BHHHEADE,ECE, CEADHEADCEADCEH ,CEH=60o, 60o

  • ().

  • 2lBBDDBClCCCDDCECEl BCElBCDl1BCD=45 BCE=13545135C.

  • 8.P1DCBP1DCBCDP1DP1D=6BC=3DC=3AP1D. ABP1ABPABP-CD-B45EFABPD.(1)AFPEC(2)P-BC-AEFP..:1PCG,.GFGEG,FG//CD,FG= CD,AE//CD,AE= CDAE//FG,AE=FG,AEGF,AF//EG,EG PEC,AF//PEC

  • 8.P1DCBP1DCBCDP1DP1D=6BC=3DC=3AP1D. ABP1ABPABP-CD-B45EFABPD.(1)AFPEC(2)P-BC-AP:2CDPAD,PADABCDPABP-BC-A,RtPAB,PA=3,PB= ,PA=AD,PDA=45o,PAADPAABCD,ABBC PBBCsinPBA=60o

  • .

  • 9.ABCDA1B1C1D1EBCB1D1EABCD.ADBCB1A1D1C1.E:, ,.:B1C1M,.MEM,EBC,EMA1B1D1,B1D1 MD1B1E,B1D1EA1B1C1D1,ABCD//A1B1C1D1,B1D1EABCD, a,

  • 9.ABCDA1B1C1D1EBCB1D1EABCD.ADBCB1A1D1C1.F:BCF,.MBDEF,.EEBC,EF//BD,BD//B1D1,EF//B1D1,EFB1D1ABCDEB1D1F=EFBGEFFEG,GB1G,B1GBB1D1EABCD a,BE= BG= RtB1BG,B1G=

  • ABC-A1B1C1MNAA1BB1B1N=A1B1=2A1MC1MNA1B1C1

  • SABCSA=SB=SCASB=BSC=CSA=90MNABSCSMBN.Paaa

  • 1.1 2 3

  • 4 5 6

  • 2. 1 2 3

  • ABCA1B1D1C1AC11,(1)ACD1D

  • ABCA1B1D1C1AC11,(1)ACD1D(2)ABD1

  • ABCDA1B1C1D1HAC1AB=aAA1=AD=bC1BDC1H=

  • ABCDEFCDFEABFEEF=5,AD=13,ABCD

  • P-ABCPA=PB=PCPABCPABCOOA=OB=OCOABC

  • P-ABCPA,PB,PC,PABCPABCOABCDO

  • P-ABCPABC,PABCPABCOABCOEF

  • P-ABCPA=PB=PCPABCP-ABCPA,PB,PC,PABCP-ABCPABC,PABCPABCO

  • ABCA1B1D1C1AC11,D(1)AA1B1CD

  • ABCA1B1D1C1AC11,D(1)AA1B1CD(2)ABB1D1

  • 1PABCPABCABCOP

  • 4.PABCPAPBPCPAPBPC3PABC

  • 3.ABOPAOCAB5AC2BPAC

  • PABCEFO

  • ABEFDCPZ

    3ABCD4EFABADPC

    ABCDPC=2

    1CPEFAPEF3

    2BPEF

    _1139904825.unknown

  • l l AA`BB`l

  • lA`AB

  • ABCDA,B,C,DABCD4ABCD3

  • 5.ABCDABCDAA=5AB=12BCABCD

  • ABCDPFEABCD4EFADABPCABCDPC=2BPEFGOH

  • 3ABCD4EFABADPCABCDPC=2BEFPACBDO,ACEFHOHPHBDPEFBBDOOKPEFOKKOKHPCH OK

  • ABAB AABB

  • :1 ,M,N,E,F .(1): ;(2): .

  • 1999ABCD-ABCDEDDEACDBEACABCD450AB=a1EAC2ABAC

  • 1600M--NPPMN12PaPAPBMNABPAPB,aQPQ=xPAQsinAQP=1/xRT PBQsin AQP=2/xcos600=cos(AQP +AQP)x

  • 2ABCDBAD=600AB=10PAABCDPA=51PCD2PBD3PAD4PCPAD(1)PCDCDEAEE(2)BDACOPOO

  • 1. ab ab d1 d2 ( )(A)d=d2 (B)dd2 (C)d1d2 (D)dd2DC

  • 3. ABCAB=9AC=15BAC=120ABC

    PABC14

    P ( )

    (A)7 (B)9 (C)11 (D)13A

  • 5.RtABCC ABAB=26ACBC45 30AB______.26.- l A l

    2 , 1 ,

    __________________30o 150o

  • 2.ABCDABACAD6BC3CD4BD5ABCDABD

  • 7.MON=60POPO=3POMON45P

    A.B. C. D.A8. EF ABCDEF

    15AB17ABCD

    28EFCD 2539

  • 9. , AB, AB, A , B a b , abA a 2B b 5AB=4ab ababABAB

  • ACDBA1B1D1C1O ACBDO AOBD AODD1 AOBD1 AO

  • ACDBA1B1D1C1OEA1ACC1AB1D1 AA1CC1A1 CO1A A1EAO1E A1EAB1 D1 A1E

  • ACDBA1B1D1C1EF..A1CAB1D1 A1CBC1DA1CAB1D1BC1DEFEF

  • ACDBA1B1D1C1G.ABCDA1B1 BCDA1B1 BG(GBC1B1CBGB1C, BGCD BGA1B1CD :

  • (1)..

    (2).

  • 12. aABCDABC=60PCABCDEPAEPBC.:EPAEPBCA PBC.PCABCD,PBCABCDABCDAHBCBCH,AH= H

  • 12. aABCDABC=60PCABCDEPAEPBC.GO

  • ()

    .

  • PMN PM=3cm,PN=4cm,PMNlQ llQMlQNMQNlMQN=120M+N=180PMQNMPN=180120=60MN=

  • ()VSh

  • ()

  • (1) 1.(2)

  • (2)2.(3).(1)3.(1)....(2)abc l l2=a2+b2+c2

  • VSh/3

  • ()12

  • PCBDARt PEHRt PHBRt PEBRt BEH

  • 1234

  • 1234PABC567

  • 1.( )

    (A)

    (B)

    (C)

    (D)C

  • 2.. ( )(A)0 (B)1 (C)3 (D)5C

  • 2.ABC-A1B1C1AB=2 BB1AB1

    C1B

    A.60o B.90o C.105o D.75o

    B

  • 3.a+b+c=611 __ 3045 ___ sinsinsin_____ ___________________________.sin2+sin2+sin2=2530

  • 8cm2,S=2

  • ,()

  • (

  • a.b,PABCO

  • 1.60,PABCO

  • 1.60,PABDCO

  • a .60,30PABCO

  • :P-ABC,AB=AC=10,BC=12,45,?

  • aPABC

  • a,hABDCOPHx

  • P-ABC4

  • 4. P-ABCDPAABCDABC=90PA=AB=BC=2AD=1, (1)DPBC (2)PABPCD: (1)AD//PBCDPBCAPBCPABC, ABBCBCPABPBCPABAPBAPBCPA=AB=2, PAAB,APBDPBC

  • 4. P-ABCDPAABCDABC=90PA=AB=BC=2AD=1, (1)DPBC (2)PABPCDQ (2)CDBAQ,ADBC, AD= BCAQB,PA=AB=AQBQPQ,BCPAB,CPPQ,CPB,PCDPCD

  • 1P-ABCDaPBABCD.(1)PADABCD600 PBABCDBAADPAADPABPADABCDPAB600

  • 1P-ABCDaPBABCD.(2)PBPADPCD900.MPADPCDCMPDMMACDMADMAMCMAMD900AMC.ACAMCcosAMC =AMC900.

  • P-ABCDaBCD600PBABCD.PADABCD600E

  • P-ABCDaBCD600PBCABCDPBC. PADABCDE

  • 2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2 (1)DE

  • 2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2(2)A-BD-C() ABC-A1B1C1ACBCACBB1C1CCMBDMAMAMCACMAC2ACCM

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (1)A1BABD()BGEBG

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDAB

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDADEAA1B1BADEAA1B1BAEA

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDBC

  • 1234

  • C1.8cm2

    ()( )

    (A)4cm2 (B) cm2 (C)2cm2 (D) cm22. ( ) (A)1 : 4 (B) 1 : 3 (C) 1 : 8 (D) 1 : 7 C

  • A3.a,b,c

    245 2

    ( )

    (A) (B) (C) (D)

  • C4.S

    a ( )

    (A) (B) (C) (D)5.2340P-ABCAPBPCEFAEF ( )

    (A) 6 (B) (C) 36 (D) A

  • PP A B C D

  • ABCDAAOPPAPBPCPD Ph1h2h3h4ABCD

  • 6.A1B1C1ABCABCAB=AC=10cmBC=12cmA1ABCAA1=13cm.BBDAA1DCDDAA1=A1B=A1CABCA1ABCOBCAEOEBCAA1,B1BCC1AA1BCAA1BDAA1BDC,AA1CDA1ABA1FABFFRtA1FAA1A=13AF=5A1F=12,BD=ABsinA1AB=10S=(BD+DC+BC)A1A=396,ABCAEBCAB=10BE=6,AE=8,SABC=8,S=396+248=492(cm) 2

  • 7.EFaABCDA1B1C1D1A1ACC1C1B1EDF....FE::A1C1, B1D1O1,O1O1O1H B1DH,HEF//A1C1, A1C1//B1EDF C1B1EDF A1C1 B1EDFB1D1DB1EDF,O1HB1EDF O1H B1O1HB1DD1

  • 7.EFaABCDA1B1C1D1A1ACC1C1B1EDF...FE::EFB1C1EFh1,DC1EFh2 , h1+h2=B1D1=2a ,

  • 7.EFaABCDA1B1C1D1A1ACC1C1B1EDF...FE::

  • aABCDACBDaD-ABCABCD

  • aABCDACBDaD-ABCABCD

  • ABCD-A1B1C1D1EFBB1DD1a,D1-AEC1FEF

  • ,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1A1B1C1D1ABCD

  • A1B1C1D1ABCD,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1

  • 2A1B1C1D1ABCDV= SA1B1CD1CE,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1

  • A1B1C1D1ABCDSB1CD1=2,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1

  • A1B1C1D1ABCDSB1CD1=V= ( 2 SB1C1D1)h2,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1

  • a.

  • 18 3

  • SQ

  • PABCP-ABCPA=a, PB=b, PC=c , ABCSPABC

  • ABCDPFE:ABCD4,E,FADABPCABCDPC=2BPEFGOH

  • ABCDPFEG:ABCD4,E,FADABPCABCDPC=2BPEF

  • ABC-A`B`C`BB`C`CSAA`a

  • ABCA`B`C`ABC-A`B`C`BB`C`CSAA`a

  • ,ABCDEF,ABCD3,EF//AB,EF=1.5, EFAC2,=4.5=3

  • =6=1.5,ABCDEF,ABCD3,EF//AB,EF=1.5, EFAC2,

  • ABC-A1B1C134ABB1C1

  • 43

  • 43

  • P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60

  • P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60

  • P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60

  • P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60

  • P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60

  • :S ABC,EFSBSC AEFSCB.SABC SOAOBCD SDEFGAG.

    GO

  • ABCSD1

  • ABCSEFKEY

  • aABCD-A1B1C1D1D1C1BDABCDA1B1C1D1 = KEY

  • ABCDA1B1C1D1AD=AA1=1AB=2EABD1EA1DEAB,EACD1AED1ECD

  • PBCDEAPABCD PBADPAD2ABCDPADABCD120PABCDAPBCPB,,..

  • 18 cm2,3cm.,OABCOODBCABACDEDEDEF VBCABVACVDFEF

  • AGV= AOF=600

  • D

  • C

  • 4. ( ) (A)1 : 4 (B) 1 : 3 (C) 1 : 8 (D) 1 : 7 C

  • A

  • C

  • A

  • 8. ABCDEAEABCBDAEAC=AB=BC=BD=2AE=1FCD(1)EFBCD(2)ABCDE(3)CDEABDE..

  • 9.P-ABCPAPBPC60PA=aPB=bPC=cP-ABC.

  • 10.A1B1C1ABCABCAB=AC=10cmBC=12cmA1ABCAA1=13cm..BCDAA1.E

  • 1.2.1/3.

  • 3012 A5400 B6480 C7200 D7920 E+2=V+F

  • .

  • AC3.45o

    90o

    ______

  • C4. 2 A. 2 B.2 C.22 D.45.2_____________6.PABCOPAPBPC

    PA=PB=PC=a, OABC

    ______________

  • 7.ABCFDE aAEF BFDF ABEADE BFAEDFAE, BFDB-AE-D BDFBF=DE= BD= - arccos

  • A-BCDAB=CD=6,5 .ECDEAEBECDAECDBECDABEAD=5,DE=3AE=BE=4ABE37VA-BCD=VC-ABE+VD-ABE12 rVA-BCD= (SABC+SBCD+SCDA+SDAB)r= 48r =16r 16r=67

  • .

  • OO2O1

  • 9.14cm 64cm2 36cm2.R111R2-36-R2-64=14 222R2-36 +R2-64=14 R=10 S=4R2=400(cm)2

  • 14

  • 14

  • HO

  • R

  • MMAMBMCMABC2MAMBMC MAMBMCd=4MA2+MB2+MC2=d2=16.

  • RMAMBMC.(1)MA2+MB2+MC2(2)M-ABC.(1)MAMBMC..MA2+MB2+MC2=4R2..

    (2).

  • 1..2. !

  • AA2.VF( ) (A)2F+V=4 (B)2F-V=4 (C)2F+V=2 (D)2F-V=2

  • A3.2030.( ) (A)2160 (B)5400 (C)6480 (D)7200A4.31( ) (A)16 (B)17 (C)18 (D)19

  • A

  • BCAD ABD ACD1BDCD2 BAC=60.ABCD

  • EFABCDBCCDAEEFAFABE ECFAFDBCDP, 1AP EF 2A-EF-P

  • 1APPFAP PE PEPE=P APPEF EF PEF AP EF.

  • 2EFHPHAHPE=PFAE=AF AH EFPH EF AHPA-EF-P(1)AP PEFPH PEFAP PH APHRt.

    cosAHP= AHP=arcos A-EF-Parcos

  • ABCDAB=3BC=4BDA-BD-CABCDBC 1ABCD 2 ABCD

  • 3RtABCAB=3BC=4EACBEABEA-BE-CACABE

  • 1ABCD-A1B1C1D1AB=3BC=2AA1=1AC1 A B C D

  • 2

  • 5.BMEDCNBECNBM60DMBN

  • 1,,,

  • 2,,

  • ABCDFD ( )

    B

  • ABCD-A1B1C1D1__________()

  • .P1P2P3. ( )(A)P3P2P1(B)P3P2=P1(C)P3=P2P1(D)P3=P2=P1 D

  • CH44(4).4cos ( )(A)-1/3 (B)1/3(C)-1/2 (D)1/2A

  • xoyABCD(50)(-30)(0-4)(-4-3)y.(1)ADBC(2)BCODEEFADFEFADBCEF(3)C-AOD.ADBC.

  • 1121223 33.12

  • 200243.1234

  • 5.()P-ABCPPAPBPCP1P2P3(())P1P2=P2P3.(1)P-ABCPABC.(2)P1P2=26P1P3=20P-ABC.

  • 1P-ABCDaPBABCD.(1)PADABCD600 PBABCDBAADPAADPABPADABCDPAB600

  • 1P-ABCDaPBABCD.(2)PBPADPCD900.MPADPCDCMPDMMACDMADMAMCMAMD900AMC.ACAMCcosAMC =AMC900.

  • P-ABCDaBCD600PBABCD.PADABCD600E

  • P-ABCDaBCD600PBCABCDPBC. PADABCDE

  • 2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2 (1)DE

  • 2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2(2)A-BD-C() ABC-A1B1C1ACBCACBB1C1CCMBDMAMAMCACMAC2ACCM

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (1)A1BABD()BGEBG

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDAB

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDADEAA1B1BADEAA1B1BAEA

  • 3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDBC

  • 2DA1C1B1DAA1C1CAB1DAA1C1CA1A1GADADGA1GAB1DA1A1HAB1HHGAB1HGA1HGA1B1AD

  • ABCDA1B1C1D1A1B1C1D1AC1AEC1FABCD

  • ABCA1B1C1AB1BC1AB=CC1=aBC=b1EFAB1BC1 EF//ABC2A1C1AB3B1ABC1.

  • 1EFAB1BC1EF//ABC

  • 2A1C1AB2A1B ABCA1B1C1 AA1ABAB=CC1=AA1 ABB1A1AB1BA1 AB1BC1 AB1A1BC1 A1C1AB1A1C1AA1 A1C1ABB1A1 A1C1AB

  • 3B1ABC1. 3 A1B1//AB A1B1//ABC B1ABC1A1ABC1 A1A1HAC1H2 BAACC1A1

  • B1ABC1

  • aABCD-A1B1C1D1EFABBC(1)B-FB1-E(2)DB1EF(3)DD1MBMEFB.M.B1EFDD1M.B1BDD1B1EFB1BDD1B1EF=B1GB1BDD1BMB1GDD1MBMB1EFB1BGBDMMDD1M...

  • M

  • BC

  • 05PABCABBCABBCkPAODACPCOPABC()k PAPBC() kOPBCPBC

  • P-ABCPACABC PA=PB=PC=3 1AB BC 2AB=BC= ACPBC . 2004EF

  • PADPCDACPBAMCBMC 1.0518P-ABCDABDC ABCDPA=AD=DC= AB=1MPB

  • 3D-AB-EABCD2AEEBFCEBFACEAEBCEB-AC-EDACE

  • PABCDABCDPAABCDAB= BC=1PA=2EPD.ACPBPABNNEPACNABAP.