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第三单元 函数及其图象. 第 18 课时 几何初步及平行线、相线 第 19 课时 三角形 第 20 课时 全等三角形 第 21 课时 等腰三角形 第 22 课时 直角三角形与勾股定理 第 23 课时 相似三角形 第 24 课时 相似三角形的应用 第 25 课时 锐角三角函数 第 26 课时 解直角三角形及其应用. 第四单元 三角形. 第 18 课时 ┃ 几何初步及平行线、相交线. 第 18 课时 几何初步及平行线、相交线. 考点聚焦. 第 18 课时 ┃ 考点聚焦. 考点 1 三种基本图形 —— 直线、射线、线段. 一. 线段. - PowerPoint PPT Presentation
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181920 21 22 23 24 25 26
18
18 1
________________ ________
2 18
1__________________2______ ________ (1)(2)
3 18
1 n ________ 2 n() ________ 3 n______ 4 n________ 5 n ________
eq \f(nn1,2)
eq \f(nn1,2)
eq \f(nn1,2)
eq \f(nn1,2)
eq \f(n2n2,2)
4 18
5 18
6 18
7 18
18 1. 2. 1 [2012] 181ABCDOOMAOCBOD76BOM() A38 B104 C142 D144181C
18
[] AOCAOM180
BOD76AOCBOD76.
OMAOC
AOMeq \f(1,2)AOCeq \f(1,2)7638
BOM180AOM18038142.
C.
123 2 [2011] 3635________14325 [] 180363514325. 18
90180.18
1. 2. 3. 3 182ABCDAPCPABPCD18218
APC PAB PCD APC360(PAB PCD) APCPAB PCD APCPCDPAB. APC PAB PCD. PPEABAAPE. ABCDPECDCCPE PAEPCDAPECPE APC PAB PCD.
18
19
19 1
2 19
1
eq \b\lc\{(\a\vs4\al\co1(,\b\lc\{(\a\vs4\al\co1(,))))
2
eq \b\lc\{(\a\vs4\al\co1(,\b\lc\{(\a\vs4\al\co1(,))))
3 19
4 180 360 19
5 19
6 19
19 1. 2. 3. 1 [2012] 3 cm4 cm7 cm9 cm() A1 B2 C3 D4B
[] B 347349 379479 379479 B.19
1. 2. 2 [2012] 191ABC DEABACB50.ABCDEAA1BDA1________
19180 19
[] DEBCADEB50ADEA1DEBDA11802B80.19
19
1. 2. 19 3 [2012] 192ACDABCABCACDA1A1BCA1CDA2An1BCAn1CDAn. A.(1)A1________ (2)An________192
eq \f(,2)
eq \f(,2n)
19
[] (1)A1BCeq \f(1,2)ABCA1CDeq \f(1,2)ACDACDAABCA1CDA1BCA1
19
(2)(1)A2eq \f(1,2)
A1BABCA1CACD
A1BCeq \f(1,2)ABCA1CDeq \f(1,2)ACD.
ACDAABCA1CDA1BCA1,
eq \f(1,2)(AABC)A1BCA1A1eq \f(1,2)A.
AA1eq \f(,2)A2eq \f(1,2)A1eq \f(1,2)eq \f(1,2)eq \f(,22)
Aneq \f(,2n).
19
20
20 1
________ ________ (1) (2)
2 20
3 ASA AAS SAS HL 20
4 20
20 1. SSSASAAASSASHL2. 1 [2012] 201ABAE12B EBCED.201
121BAD2BADBACEAD.BACEAD
BACEADBCED. [] 12EADBACABAEBEASAABCAEDBCED.20
1() 2 320
1. 2. 3 2 [2012] 202ABCDBCADADEFCEBF.BDFCDE________()20220
DEDF(CEBFECDDBFDECDFB) BDFCDE BDFCDE.20
[] EDCBDFDCDBDEDF(CEBFECDDBFDECDFB)20
()20
12 3 [2012] ac. ABCBCaABc ABC. 20320
21
21 1 1
____ ____1(________) 2________ (1)(2)(3)(4)(5)(6)(7)
2 21
3 60 3 21
4 21
5 21
21 1. 2. 3. ().
1 211ABCABACADBCABCBGADEEFABF. EFED.ABACADBCADBC.BGABCEFABEFED. [] ADBCEFAB21121
(1) (2) 21
2 [2011] 212ABCBDCEOOBOC. (1)ABC (2)OBAC21221
(1)OBOCOBCOCB.BDCEBDCCEB90.BCCBBDCCEB (AAS)DCBEBC, ABAC.ABC (2)OBAC AO. BDCCEBDCEB. OBOCODOE. ADOAEO90AOAOADOAEO(HL) DAOEAO OBAC
21
[] (1)BDCCEB DCBEBC (2)AOHLADOAEODAOEAO21
(1)(2)(3)21
1. 2. C 21
3 [2012] ABCADBCDADeq \f(1,2)BCABC()
A45 B75
C4575 D60
21
[] BACBAC
(1)ABACADBCBDCDeq \f(1,2)BCADB90.
ADeq \f(1,2)BCADBDB45ABC45
(2)ACBCADBCADC90.
ADeq \f(1,2)BCADeq \f(1,2)ACC30.
CABBeq \f(180C,2)75
ABC75.
ABC4575.
C.
21
4 [2011] ABCEABDCBEDEC213.AEDB21321
ABCABCACBBAC60ABBCAC.EFBCAEFAFE60BACAEFAEAFEFABAEACAFBECF.ABCEDBBED60ACBECBFCE60EDECEDBECBBEDFCE.DBEEFC120DBEEFCDBEFAEBD.21
ABCABCACB60ABD120.ABCEDBBEDACBECBACEEDECEDBECBBEDACE.FEBCAEFAFE60BACAEFEFC180ACB120ABD.EFCDBEDBEF.AEFEFAEAEDB.21
(3) ABCEABDBCEDEC.ABC1AE2CD()
13. 21
6021
1221
21521
5 (a)(b)(c)1.(a)(b)(c)
(1)48
(2)10
(3)2eq \r(,2)6
(a)(b)(c)21
[] (1)484(2)102eq \r(5)(3)2eq \r(2)62eq \r(2)
. 21
22
22 1
________ (1) (2)30 ______________ (3) ______________ (1) (2)
2 a2b2c2 a2b2c2 22
3 22
4 22
5 1()()() 2________ 3________ 22
22 1. 2.
D 22122
1 [2011] 453 cm30221()
A3 cm B6 cm
C3eq \r(2) cm D. 6eq \r(2) cm
22
[] AADBDD
AB2AD236(cm)ABCACeq \r(2)AB6eq \r(2) cm.
(1) (2) (3)22
1. 2. 2 222()AC1 (1) (2)AB4BC4CC15 (3)B122222
22
(1)ACC1A1ABC1D1.
AC1AC1.
(2)A1B1C1
l1eq \r(42452)eq \r(97).
BB1C1
l2eq \r(44252)eq \r(89).
l1>l2l2eq \r(89).
(3)B1EAC1E
B1Eeq \f(B1C1,AC1)AA1eq \f(4,\r(89))5eq \f(20,89)
eq \r(89)
B1eq \f(20,89)
eq \r(89).
22
D 22
3 [2012] 2343451eq \r(3)2.()
A B
C D
22
[]
22321342
324252
12(eq \r(3))222
.
D.
22
23
23 1 abcd
abcd____________
2 adbc b2ac 23
(1)eq \f(a,b)eq \f(c,d)________
(2)adbc(abcd0)eq \f(a,b)______
eq \f(a,b)eq \f(b,c)________bac
eq \f(a,b)eq \f(c,d)eq \f(ab,b)______
eq \f(c,d)
eq \f(cd,d)
3 23
eq \f(AC,AB)eq \f(BC,AC)
eq \f(\r(51),2)(0.618)
4 23
5 23
6 23
23 12 1 [2012] 231PABPAPB.S1PAS2ABPBS1________S2.()231
[] PABPAPB PA2PBAB. S1PAS2ABPB S1PA2S2PBAB S1S2.23
123 2 232ABCADEBADCAEABCADE. (1)() (2)23223
23
(1)ABCADEABDACE.
(2)ABCADE.
BADCAE
BADDACCAEDAC
BACDAE.
ABCADE
ABCADE.
ABDACE.
ABCADE
eq \f(AB,AD)eq \f(AC,AE).BADCAE
ABDACE.
23
[] (1)ABCADEABDACE.
(2)BACDAEABCADEABCADEABCADEeq \f(AB,AD)eq \f(AC,AE)ABDACE.
23
1 2 323
23323
3 233ABCDEFABACBCDEBCDFAC.eq \f(AD,BD)eq \f(2,3)SABCaDFCE
23
DEBC
ADEABC.
eq \f(AD,BD)eq \f(2,3)eq \f(AD,AB)eq \f(2,5)
SADESABC425SADEeq \f(4,25)a.
SBDFeq \f(9,25)a.
SDFCESABCSBDFSADEeq \f(12,25)a.
23
SADES1SBDFS2
SABCSeq \r(S1)eq \r(S2)eq \r(S).
24
24 1
(1)(2)(3)(4)
2 24
24
1 [2012] 241DEFABDFDEBDE40 cmEF20 cmDFAC1.5 mCD8 mAB________m.2415.5 24
24
[] DEFBCD90DD
DEFDCB
eq \f(BC,EF)eq \f(DC,DE).
DE40 cm0.4 mEF20 cm0.2 mCD8 m
eq \f(BC,0.2)eq \f(8,0.4)
BC4 m
ABACBC1.545.5(m)
24224
2 [2011] 242ABCADBCBC40 cmAD30 cmHGHE2EFGHEFBCGHACABADHGM.
(1)eq \f(AM,AD)eq \f(HG,BC)
(2)EFGH
24
(1)EFGH
EFGHAHGABC.
HAGBACAHGABC
eq \f(AM,AD)eq \f(HG,BC).
(2)(1)eq \f(AM,AD)eq \f(HG,BC).HExHG2x
AMADDMADHE30x
eq \f(30x,30)eq \f(2x,40)x122x24.
EFGH2(1224)72(cm)
[] (1)AHGABC (2)HExHG2x24
243D 24
[2011] 243ABCABACDEABACGFBCDEFGDE2 cmAC ()
A3eq \r(3) cm B4 cm
C2eq \r(3) cm D2eq \r(5) cm
24
3244ABCDMNDMNCABCDAB4. (1)AD (2)DMNCABCD24424
24
(1)MNABMDeq \f(1,2) ADeq \f(1,2)BC.
DMNCABCDeq \f(DM,AB)eq \f(MN,BC)
eq \f(1,2)AD2AB2
AB4AD4eq \r(2).
(2)DMNCABCDeq \f(DM,AB)eq \f(\r(2),2).
25
25 1
RtABCC90ABcBCaACbA
A
sinAeq \f(A,)
________
cosAeq \f(A,)
________
tanAeq \f(A,A)
________
eq \f(a,c)
eq \f(b,c)
eq \f(a,b)
2 1 25
eq \f(1,2)
eq \f(1,2)
eq \f(\r(3),2)
eq \f(\r(3),2)
eq \f(\r(3),3)
eq \f(\r(2),2)
eq \f(\r(2),2)
eq \r(3)
3 01 () () 25
eq \f(sinA,cosA)tanA
25 1. 2. 3.
251B 25
1 [2012] 251ABCsinA()
A.eq \f(1,2) B.eq \f(\r(5),5) C.eq \f(\r(10),10) D.eq \f(2\r(5),5)
25
[] CDABO
CDAB
RtAOC
COeq \r(1212)eq \r(2)
ACeq \r(1232)eq \r(10)
sinAeq \f(OC,AC)eq \f(\r(2),\r(10))eq \f(\r(5),5).B.
25
1. 3045602. 75 25
2 [2012] ABCABeq \b\lc\|\rc\|(\a\vs4\al\co1(cosA\f(1,2)))eq \b\lc\(\rc\)(\a\vs4\al\co1(sinB\f(\r(2),2)))
eq \s\up12(2)0C________.
25
[] eq \b\lc\|\rc\|(\a\vs4\al\co1(cosA\f(1,2)))eq \b\lc\(\rc\)(\a\vs4\al\co1(sinB\f(\r(2),2)))
eq \s\up12(2)0
cosAeq \f(1,2)0sinBeq \f(\r(2),2)0
cosAeq \f(1,2)sinBeq \f(\r(2),2)
A60B45
C180AB180604575
75.
1. 2. 25225
3 [2012] 252RtABC
ACB90DABBECDE.AC15cosAeq \f(3,5).
(1)CD
(2)sinDBE
25
(1)AC15cosAeq \f(3,5)AB25CDeq \f(25,2)
(2)CD BDECBABC
cosECBcosABCeq \f(4,5).
BC20EC16EDeq \f(7,2).
BDeq \f(25,2)sinDBEeq \f(7,25).
4 [2011] (1)253ABCC90ABC30ACmCBDBDAB. D tan75 (2)M(20)MNyNOMN75.MN25325
25
(1)D15tan752eq \r(3)
(2)M(20)N(042eq \r(3))MNy(2eq \r(3))x42eq \r(3).
26
26 1 c2 90
532 RtABCC90 (1)a2b2________ (2)AB________ (3)sinAcosB________ cosAsinB________tanA________ (4)sin2Acos2A1 (1) (2) (3)(ca) (4)ab
eq \f(a,c)
eq \f(b,c)
eq \f(a,b)
2 hl 26
26 ()1. ()2.
26
1 [2012]
45.
30.
1.6 m.
20 m.
(eq \r(2)1.414eq \r(3)1.732)
26
BCDAE.
AExRtACEACE45AEB90
CAE45AECEx
RtABEB30AEx
tanBeq \f(AE,BE)tan30eq \f(x,BE)
BEeq \r(3)x.BECEBCBC20
eq \r(3)xx20x10eq \r(3)10.
ADAEDE1010eq \r(3)1.628.9()
28.9
[] BCDAE.AExRtACECEAERtABEBEBECEBCAEADAEDE.26
26126
26226326
1. 2. 26
2 [2012] 264AB12/. 601.5C()26426
26
CCDABD.
RtBDCBC121.518()
CBD904545
CD18sin459eq \r(2)()
RtADCCAD906030
AC2CD18eq \r(2)()
18eq \r(2)
1. 2. 3 [2012] 265ABCDAD.(iCEEDm)26526
26
BBFADBCEF.
EFBC4BFCE4.
RtABFAFB90AB5BF4.
AFeq \r(5242)3.
RtCEDieq \f(CE,ED)eq \f(1,2)
ED2CE248.
ADAFFEED34815()
[] BFADFABFAFCEDEDAD26
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