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

(1) EAB214AEDB AE________DB(>

(2) AEDBAE________DB(>

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