Геометрия7_9
.pdf7 KJiaC |
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3. .D;aHo a II b II c II d. |
.D;osep;iTL, ~o a II d. |
4.IlpaMi AB i CD napaJieJILHi• .D;osep;iTL, ~o KOJIH uip;piaoK BC nepeTHHae npaMy AD, TO TO'IKanepeTHHY HaJie:>KHTL ui,ZJ;piaKy
AD (MaJI. 70).
5. .D;aHo TPHKYTHHK ABC. Ha CTOpoHi AB noaHa'leHoTO'IKYB 1, a Ha CTopoHi AC - TO'IKYC1 (MaJI. 87). HaauiTL BHyTpimHi
OAHOCTOpoHHi i BHYTPimHi piaHocTopoHHi KYTH npH npSIMHX AB, AC i ci'IHiiiB1C1.
6.HaauiTL BHYTPimHi piaaocropoHHi i BHyTpimHi op;HocTopoHHi KYTH Ha MaJIIOHKY 72.
7.Bi,ZJ;piaKH AD i BC nepeTHHaIOTLCH. ,IJ;JIH npHMHX AC i BD i ciqHol BC HaauiTL napy BHYTPimHix piaHocropoHHix KYTiB. ,Il;JIH n;ux me npSIMHX i ci'IHOIAB HaaBiTL napy BHYTPimHix op;HoCTOpoHHix KyTiB. IlOHCHiTL Bi,ZJ;nOBi.,ZJ;b.
8.,Il;aHo npaMy AB i TO'IKYC, SIKa He Jie:>KHTL Ha n;iii npaMiii.
.D;osep;iTL, ~o qepea TO'IKYC MO:>KHa npouecTH npHMy, napa-
JieJILHy npHMiii AB.
9. .D;ouep;iTL, ~o 6iceKTpHCH BHYTPimHix piaHOCTOpOHHix KyTiB, yTBOpeHHX napaJieJILHHMH i ci'IHOIO,napaJieJILHi, T06To JiemaTL
Ha napaJieJILHHX npSIMHX.
10.Bi,ZJ;piaKH AB i CD nepeTHHaIOTLCH B roqn;i E i p;iJIHTLCH n;ie10 TO'IKOIOnonoJiaM• .D;oue,11;iTL, ~o npaMi AC i BD napaJieJILHi.
11.TpHKYTHHKH ABC i BAD piBHi. To'IKHCi D Jie:>KaTL no piaHi 6oKH uip; npSIMol AB• .D;oue,11;iTL, ~o npaMi AC i BD napaJieJILHi.
12. KyT ABC ,11;opiBH10e 80°, a KYT BCD - 120°. 1IH MO:>KyTL npaMi AB i CD 6yTH napaJieJILHHMH? 06rpyHTyiire ui.,ZJ;noBiAJ>.
13. IIpaMi AC i BD napaJieJILHi, npH'IOMyTO'IKHAi D Jie:>KaTL no piaHi 6oKH ui,ZJ; ci'IHOIBC (MaJI. 77). .D;oue,ZJ;iTL, ~o: 1) KYTH DBC i ACB BHYTPimHi piaHOCTOPOHHi Bi.,ZJ;HOCHO Ci'IHOIBC; 2) npoMillL BC npoxop;HTL Mim cropoHaMH KyTa ABD; 3) KyTH
CAB i DBA BHYTpimHi O,ZJ;HOCTOPOHHi Bi,ZJ;HOCHO Ci'IHOI AB. 14. 1) PiaHH~ p;uox BHYTpimHix O,ZJ;HOCTOpoHHix KYTiB npH p;uox napaJieJILHHX npSIMHX i Ci'IHiHp;opiBHI06 30°. 3Haii,ll;iTL n;i KYTH.
2) CyMa ,11;uox BHYTpimHix piaHocTOpoHHix KyTiB npH p;uox napaJieJILHHX npHMHX i Ci'IHiiip;opiBHIOe 150°. 1IoMy p;opiBHIOIOTb n;i KyTH?
15.Op;HH a KYTiB, md yTBOpIOIOTLCH npu nepeTHHi p;uox napaJieJILHHX npSIMHX ci'IHOIO,p;opiBHI06 72°. 3Haiip;iTL iHmi ciM KyTiB.
16.Op;HH a KyTiB, md yTBopIOIOTLCH npu nepeTHHi p;uox napaJieJIL-
§ 4. CyMa KYTIB TPHKYTHHKa |
61 |
HHX npHMHX Ci'IHOIO,p;opiBHIOG 30°. ~ Mome OAHH 3 pemTH ceMH KyTiB p;opiBHIOBaTH 70°? IloscHiTL B~IlOBi,D;L.
17. ,ll;oBep;iTL, m;o p;si npsMi, napaJie.nLHi nepnelfAHKYJIHPHHM npsMHM, nepneHAHKYJIHpHi Mim co6o10.
18.3aaiip;iTL Hes~oMHii KYT TpHKYTHHKa, HKm;o 8 HLOMY p;sa KYTH p;opiBHIOIOTL! 1) 50° i 30°; 2) 40° i 75°; 3) 65° i 80°; 4) 25° i 120°.
19.3Haiip;iTL KYTH TPHKYTHHKa, HKID;O BOHH nponop:o;iHHi AO 'IH-
ceJI: 1) 1, 2, 3; 2) 2, 3, 4; 3) 3, 4, 5; 4) 4, 5, 6; 5) 5, 6, 7. 20. ~ Mome y TPHKYTHHKY .OyTH! 1) ,D;Ba TYilHX KYTH; 2) TynHii i
npHMHH KYTH; 3) p;Ba npHMHX KyTH?
21.1IH Mome 6yTH TynHM KYT npH OCHOBi piBHo6ep;peHoro TPHKyTHHKa?
22.3aaiiAiTL KYT Mim 6i'IHHMHCTOpoHaMH piBHo6ep;peHoro TpHKYTHHKa, HKID;O KYT npH iioro OCHOBi p;opiBHIOG: 1) 40°; 2) 55°;
3)72°.
23.3aaii,D;iTL KYT npH OCHOBi piBHo6ep;peHoro TPHKYTHHKa, BKID;O
KYT Mi>K 6i'IHHMH CTOpoHaMH p;opiBHIOe: 1) 80°; 2) 120°;
3)30°. , ,
24.Op;HH a KyTiB piBHo6ep;peHoro TPHKYTHHKa p;opisHIOe 100°. 3Haiip;iTL pemTy KYTiB TPHKYTHHKa.
25.Op;HH a KyTiB pisao6ep;peaoro TPHKYTHHKa p;opiBHI06 70°. 3aaii,D;iTL pemTy KYTiB TPHKYTffHK&. CKiJILKH poaB'saKiB Mae aap;aqa?
26.,ll;oBep;iTL, m;o KOJIH O,D;HH 3 KYTiB piBHo6ep;peaoro TpHKYTHHKa p;opiBHI06 60°, TO TpHKyTHHK - piBHOCTOpoHHiii.
27.YpiBHo6ep;peHOMY TPHKYTHHKY ABC 3 OCHOBOIO AC nposep;eHo
A |
[ |
Man. 87 |
Man. 88 |
7 KJiac |
62 |
6iceKTJ>HCY CD. 3HaiiJtiTi. KYTH TJ>HKYTHHKa ABC, RKm;o KYT |
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ADC p;opiBHIOe: 1) 60°; 2) 75°; 3) a.. |
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28. y piBHOOe,D;peHOMY TPHKYTHHKY ABC 3 OCHOBOIO AC i |
KYTOM |
npH sepmmti B, m;o p;opiBHIOe 36°, nposep;eao 6icel(TJ>HCY AD.
,D;ose,ltiTb, m;o TJ>HKYTHHKH CDA i ADB piBHo6ep;peHi (Man. 88). 29. Y TpHKYTHHKY ABC nposep;eHo 6iceKTPHCH a sepmHH A i B.
To11Ky ix nepeTHHY noaHaqeHo D. 3HaiiJtiTi. KYT ADB, BKm;o:
1) LA= 50°, LB= 100°; 2) LA= a, L B = ~;
3)LC= 130°; 4) LC= y.
30.'IoMyp;opiBHIOIOTb KYTH piBHOCTOpoHHbOro TpHKYTHHKa?
31.~ JIKHM KYTOM nepeTHHaIOTbCJI 6iceKTPHCH ABOX BHYTpimHix op;HocTopoHHix KYTiB npu napaJieJibHHX npsmtnx?
32.Op;ua ia aosHimHix KyTiB piBHo6ep;peHoro TPHKYTHHKa p;opis-
HI06 70°. 3Haiip;iTb KYTH TJ>HKYTHHKa.
33.3uaiip;iTb KYTH TPHKYTHHKa, 3H8IO'IH,m;o 30BHimHi KYTH npH ,ll;BOX iioro BepJUHHaX p;opiBHIOIOTb 120° i 150°.
34.Asa aosuimHix KYTH TJ>HKYTHHKa p;opiBHIOIOTb 100° i 150°. 3uaii,ltiTb TJ>eTiii 30BHimuiA KyT.
35.Y TPHKYTHHKY ABC nposep;euo BHCOTy CD. HKa a TPbOX ToqoK A, B, D neacHTb Miac ABOMa iumuMH, BKID;O KYTH A i B TJ>HKYTHHKa l'OCTpi?
36.Y TPHKYTHHKY ABC nposep;euo BHCOTY CD. HKa a Tpi.ox roqoK
A, B, D nemHTb Miac ABOMa iHmHMH, BKID;O KYT A TynHii? 0614pyHTyHTe Bip;noBi,ll;b.
37.Aosep;iTi., m;o 6iceKTpHca aosuimai.oro KyTa npH sepmHHi piBHo6ep;peuoro TJ>HKYTHHKa napaJieJlbHa OCHOBi.
38.CyMa aosaimHix KYTiB TJ>HKYTHHKa ABC npu sepmHRax A i B, BMTHX no O,ll;HOMy AJIJI KOXCHOl BepmHHH, p;opiBHI06 240°. 'IoMyp;opiBHIOe KYT C TPHKYTHHKa?
B
0 |
A |
[ |
E |
Man. 89
§ 5. |
reoMeTpH'IHi IIOOYAOBH |
63 |
39. |
,D;aHo TpHKYTHHK ABC. Ha npoAOBmeHHi CTOpoHH AC BiAKJia- |
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AeHo siApiaKH AD = AB i CE = CB (11aJI. 89). HK |
aHaATH |
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KYTH TPHKYTHHKa DBE, aHaIO'IHKYTH TPHKYTHHKa ABC? |
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40. Y TpHKYTHHKY OAHH a BHYTpi.mHix KYTiB AOPiBHIOe 30°, a OAHH |
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ia aOBHimHix 40°. 3aaiiAiTL pemTY BHYTPimHix KYTiB TPHKYT- |
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HHKa. |
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41. |
3 sepmHHH npsMoro KyTa TpHKYTHHKa ABC nposeAeHo BHCOTY |
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BD. 3uaAAiTL KyT CBD, aHaIO'IH,~o: 1) L A = 20°; 2) |
LA= |
=65°; 3) LA= a.
42.3 sepmHHH Tynoro KYTa B TPHKYTHHKa ABC nposeAeHo BHCOTY BD. 3mUiAiTL KYTH TPHKYTHHKiB ABD i CBD, aHaIO'IH, ~o
LA= a, LB= ft
43• .D;o:eeAin., ~o B llJ>SIMOICYTHOMY TpHKY'fHHKY3 KYTOM 30°' KaTeT, npoTHJiemHBii ~MY KYTY, AOpiBmoe noJIOBHHi rinoTeayau.
44.3uaiiAiTL KYTH npgMOKYTHoro piBHo6eApeHoro TPHKYTHHKa.
45.Y piBHOCTOpoHHbOMY TPHKYTHHKY ABC npoBeAeHo MeAiaay AD. 3aaiiAiTL KYTH TPHKYTHHKa ABD.
46.BucOTH TpHKYTHHKa ABC, npoBeAeHi a sepmHH A i C, nepeTHHaIOTLCSI B TO~ M. 3uaiiAiTL L AMC, SIK~O L A = 70°,
LC= 80°.
47~ Y TpHKYTHBKY ABC MeAiaHa BD AOPiBHIOe noJioBHHi cropoHH
AC. 3aaii:AiTL KYT B TPHKYTHHKa.
48.1Ipg11a a nepeTHHae BiApiaoK BC B iioro cepeAHHi. ,D;oseAiTh, ~o TO'IKHB i C aHaxOABTbCSI Ha OAHaKosiii siAcTaHi siA nps11o'ia.
49.BiApiaoK BC neperHHae npSIMy a B TO~ 0. BiAcTS.Hi BiA TO'IOK B i C AO npsMo'ia pisui• .D;oseAiTL, ~o TO'IKa0 e cepeAHHOIO siApiaKa BC.
50.,D;oseAiTL, ~o BiACTaHi BiA 6yAh-SIKHX ABOX TO'IOKnpRMOl AO napaJieJILHOl IlpSIMOl piBHi.
51.,D;ose.zi;iTL, ~o sip;CTaHi siA BepmHH piBHOCTopoHH1>oro TPHKYTHHKa AO npSIMHX, SIKi MiCTSITh npoTHJiemHi iM CTOpoHH, piBHi.
§5. I'EOMETPHqHI IIOBYAOBH
38. KOJIO
KoJtoM aaausaGTbCSI tl>irypa, S1Ka cKJiaAaGTbCSI a ycix TO'IOK
IlJIO~, piBHOBiAAaJieHBx Bi.A .zi;aaoi TO'IKH.D;SI TO'IKaHaaHBaeThCSI ijenrpoM KOJia.
7 KJiac |
64 |
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A .-------...------..0 |
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/liaMemp |
Ma.JI. 90 Man. 91
BiACT&Hb BiA roqoK KOJia AO ii:oro :u;eHTpa H83HB86Tbca pai}iycoM
KOJia; PaAiycoM Ha3HBa6Tbca T&Kom 6yAb-$1KHH BiApi3oK, i:u;o cno-
nyqae TO'IKYKOJia 3 ii:oro :u;eHTpoM (MaJI.
BiApi30K, i:u;o cn?Jiyqae ABi TO'IKHKOJia, Ha3HBaeTi.ca xop0010.
XopAa, i:u;o npOXOAHTb '1epe3 :u;eHTp, |
H83HB86TbC$1 oiaMerpoM. |
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Ha MaJIIOHKY 91 BC - |
xopAa, AD' - AiaMeTp. |
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3 a A a 'Ia |
(3). |
.rr;oBeAiTb, |
i:u;o |
AiaMeTP |
KOJia, |
aKHH |
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npoxoAHTb |
'lepe3 cepeAHHY |
xopAH, nepneHAHKYJISpHHH |
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AO Hei'. |
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Po 3 u'a 3 a H Ha. Hexaii AB - |
xopAa |
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KOJI8 i |
c - |
i'i'cepeAHHa (M8JI. 92). TpH- |
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KYTHHK AOB piBHo6eAPeHHii 3 ocHoBolO |
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0 |
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AB. y |
HbOMY |
CTOpOHH |
OA |
i OB piBHi |
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SK paAiYCH KOJia. 3a BJI8CTHBiCTIO MeAi- |
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aHH piBHo6eApeHoro TPHKYTHHKa, npo- |
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BeAeHoi' AO |
OCHOBH, |
BiApi3oK |
(JC 6 |
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BHCOTOIO. ToMy AiaM~ KOJia, npoBeAeHHH |
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qepea cepeAHHY xopAH, nepneHAHKyJiap- |
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Man. 92 |
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HHH AO XOPAH. |
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39. KOJIO, OIIHCAHE HABKOJIO TPHKYTHHKA
KoJIO H83HB86TbC$1 onucaHUM HaBKOJIO TpHKyTHHKa, $1Klll;O BOHO
npoxoAHTb qepea yci :Horo aepmHHH.
Teo p e Ma 5.1. .l(eHTP 'ICOJUI., on.ucaHoio Ha8'1Wll.O Tpu'ICyTHu-
'ICa, e T01'1'010 n.epeTUHY n.epn.eHiJu1Cyll.11pi8 iJo CTOpiH TpU1''flTHUKa,
npoBeiJeHux iiepea cef>eiJuHu ifux cropiH.
§ 5. reoMl!TpH•IHi no6y,D;OBH |
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65 |
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~ o Be JJ. e H H H. |
Hexaii |
ABC - |
Jl,aHHii TPHKYTHHK i 0 - |
~eHTP OIIHCaHoro |
HaBKOJIO |
HhOro |
KOJia (MaJI. 93). TpHKyTHHK |
AOC - piBHoOeJJ,peHHii; y HbOMY CTOpoHH OA i OC piBHi HK paJJ,iy-
OD ~oro TpHKYTHHKa oJJ,Hoqacuo e H:oro BHCOTOIO. KOJia JiemHTh Ha rrpHMiii, HKa rreprreHAHKYJIHpHa AO cTopoHH AC i rrpoxo,ll;HTh qepea li cepeJJ.HHy. TaK caMo AOBOAHMO,
m;o ~eHTP KOJia JielKHTh Ha rreprreHAHKYJIHpax AO ABOX iHmHX CTOpiH TPHKYTHHKa. TeopeMy JJ.OBeJJ,eHo.
3 a y B a m e H H H. IlpHMY' m;o IIPOXOAHTh qepea cepeAHHY Bi,ll;piaKa rreprreHAHKYJIHPHO AO HhOro, qacTO Ha3HBaIOTh cepeiJun- y 3B7 .R3KY 3 ~M iHKOJIH rOBOpRTh, m;o
~eHTP KOJia, OIIHCaHoro HaBKOJIO TPHKYTHHKa, JielKHTh Ha rrepeTHHi cepeAHHHHX rreprreHAHKYJIHpiB AO CTOpiH TpHKYTHHKa.
Man. 93 |
Man. 94 |
t1\
v
3 a JJ. a q a .(6). ~oBeJJ.iTh, m;o cepeJJ.HHHi rreprreH,ll;HKYJIHpH JJ.O ABOX CTOPIH TpHKYTHHKa rrepeTHHaIOThCH.
Po a B'H a a H H H. Hexau ABC TpHKYTHHK i a, b -
AHHHi rreprreHAHKYJIHPH JJ.O H:oro cropiH AC i BC (MaJI. IlpHIIYCTHMO, IIPHMi a i b He rrepeTHHaIOThCH, a OTme, rrapaJieJihHi. IlpHMa AC rreprreHJJ.HKYJI.RpHa JJ.O rrpHMo'ia. IlpHMa
BC rrepneHJJ,HKYJI.RpHa JJ.O rrpaMo'ib, a TOMy i JJ.O rrpHMO'ia, ocKiJILKH npHMi a i b rrapaJieJILHi. TaKHM qHffoM, o6HABi rrp.RMi
AC i BC rreprreHJJ.HKYJIHPHi JJ.O rrpHMo'ia, a TOMY rrapaJieJILHi. A.ne ~e HenpaBHJihHO. IlpHMi AC, BC rrepeTHHaIOThC.R B
To11~i C. Mu AiHmJIH JJ.O cyrrepe11HocTi. TBepJJ.»eeHHH JJ.O- BeAeHo.
7 Knac |
66 |
40. |
}J;OTll'IHA }J;O KOJIA |
IlpnMa, w;o npOXOAHTb qepe3 TO'IKYKOJia neprreHAHKYJI.HpHO AO paAiyca, rrpoBeAeHoro B ~IO TO'IKy, Ha3HBa6TbCH ooru'lno10. IlpH
~OMy AaHa TO'IKaKOJia Ha3HBa6TbCH TO'lKOIO OOTUKy.
Ha MaJIIOHKY 95 rrpnMy a rrpoBeAeHo qepe3 TO'IKYKOJia A rreprreHAHKYJIHpHo AO paAiyca OA IlpnMa a e AOTH'IHOIOAO KOJia. ToqKa A e TO'IKOIOAOTHKY. Moa<Ha CKa3aTH TaKo»<, w;o KOJIO AOTHKaeTbCH AO rrpnMo'ia A.
0
B A
Man. 95 |
Man. 96 |
a) |
6) |
Man. 97 |
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3 a A a q a (8). ,ll;oBeAiTb, w;o |
AOTH'IHa AO KOJia He Mae |
3 HHM iHmHX CIIiJibHHX TO'IOK,KpiM TO'IKHAOTHKY. |
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Po 3 B'n 3 a H H n. Hexaii a - |
AOTH'IHaAO KoJia B TO'l~i A |
(MaJI. 96). IlpHrrycTHMO, AOTH'lllai KOJIO MaIOTb, KpiM TO'IKHA,
§ 5. reoMeTpWIHi no6yAOBH |
67 |
crriJibHY TO'IKYB, BiAMiHHY BiA A. TpHKyTHHK AOB piBH06eApeHHH a ocHoBoIO AB. Y HbOMY 6i11Hi cropoHH AO, OB - paAiYCH KOJia. OcKiJibKH y piBHo6eApeHOMY TPHKYTHHKY KYTH rrpu: ocHoBi piBHi, TO TpHKYTHHK Mae ABa np.HMHX KYTH. A u,e
HeMomJIHBO. MH AiHmJIH AO cynepe11HocTi. TBepAmeHH.H AOBeAeHo.
I'OBOp.HTb,~O ABa KOJia, .HKi MaIOTb cniJibHY TO'IKy,aoruKa101'bCJI.
B ~H TO'I~, SK~O BOHH MIUOTb B HiH cniJibHY AOTH'IHY(MaJI. ,I.I;oTHK KiJI Ha3HBa6TbC.H 8HyrpiuiniM, .HK~O u,eHTPH KiJI JiemaTb no OAHH 6iK BiA ix cniJI&HOi AOTH'IHOi(MaJI. 97, a). ,I.I;oTHK KiJI Ha3HBa6TbC.H 308HiWHiM, .HK~O D,eHTpH KiJI JiemaT& no piaHi 60KH BiA ix cniJI&Hoi AOTH'IHOi(MaJI.
41. KOJIO, BIIHCAHE B TPHKYTHHK
KoJio HaaHBae-r&cst enucanuM y TPHKYTHHK, BK~o BOHO AOTHKa-
GTbC.H AO BCiX :Koro CTOpiH. |
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Te ope M a 5.2. |
l.(eHrp |
1Co11a, |
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6nUCaH020 6 rpUICYTHUIC, e T01'1C010 |
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lU!fH?TUHY uozo 6ice1Crpuc. |
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,I.I; o B e A e H H .H. |
Hexa:K |
ABC - |
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AaHHH TPHKYTHHK, |
0 - |
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D,eHTP |
BnHca- |
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Horo B Hboro KOJia, D, E i F - |
TO'IKH |
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AOTHKY KOJia ia CTOpOHaMH (MaJI. 98). |
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IIpstMOKYTHi TPHKYTHHKli AOD i |
ADE A |
D |
8 |
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piBHi aa rirroTeHyaoIO i |
KaTeTOM. y |
HHX |
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rirroTeuyaa AO cniJibHa, |
a K8TeTH OD |
Man. 98 |
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i OE piBHi .HK paAiycu:. 3 |
piBHocTi TpH- |
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KYTHHKiB BHnJIHBae piBHiCTb KyTiB OAD i DAE. A u,e oaHa11ae, ~o
TO'IKa0 JiemHTb Ha 6iceKTPHCi TPHKYTHHKa, npoBeAeHiH 3 BepmHHH
A. TaK caMo AOBOAHMO, ~o TO'IKa0 JiemHTb Ha ABOX iHmHx 6iceKTpHcax TPHKYTHHKa. TeopeMy AOBeAeHo.
42. ~OTAKE 3AA.Aql HA IIOBY,I.J;OBY
Y aaAa'laxHa no6yAOBY AAeTbc.H npo no6yAOBY reoMeTpH'IHoi
<PirypH aa AOIIOMoro10 AaHHX KpecJistpcbKHX iHcTpyMeHTiB. TaKHMH iHcTpyMeHTaMH ua:K'lacTimee JiiHiHKa i D,HPKYJib. PoaB'.HayBaHH.H
7 KJIBC |
68 |
aap;a11i IlOJIHrae He CTiJibKH B no6yp;oBi <l>irypu, CKiJibKH y 3Haxo- p;meHHi cnoco6y, HK ~e apo6HTH, i Bip;noBip;HOMY ,ll;OBep;eHHi. 3ap;a11a BB&lK&6TbC$1 poaB'H3&HOIO,HKIIJ,O 3H&ii,a;eHO cnoci6 no6yp;OBH <l>iryp i ,ll;OBep;eHO, m,o B peayJILTaTi BHKOHaHHH aaaHa'leHHX no6yp;oB cnpaBp;i BHXO,ll;HTb <l>irypa 3 IIOTpi6HHMH BJI&CTHBOCTHMH.
3a ,ll;OilOMOrOIO JiiHiHKH HK iHCTpyMeHTa reoMeTpH'IHHXrro6yp;oB MOlKHa rrpOBeCTH ,ll;OBiJibHY rrpHMy; rrpHMy, m,o npOXO,ll;HTb 11epea p;aHy T011Ky; npHMy, m,o npoxop;HTb 11epea p;Bi p;aHi TO'IKH.HiHKHX iHWHX onepa~ii BHKOHyBaTH JiiHiiiKOIO He MOlKHa. 3oKpeMa, JiiHiiiKOIO He MOlKHa Bip;KJiap;aTH Bip;piaKH, HaBiTb HKIIJ,O BOHa Mae no- p;iJIKH.
I.J;upKyJib HK iHCTpyMeHT reOMeTpH'IHHXno6yp;oB p;ae 3MOry OIIHcaTH 3 ~eHTpoM y p;aHiii TO'I~ KOJIO p;aHoro pap;iyca. 3oKpeMa, ~Hp
KyJieM MOlKHa Bi,ll;KJiaCTH p;aHHii Bip;pi30K Ha p;aHiH IlPHMiH Bip;
p;aHOl TO'IKH.
PoarJIHHeMo HaiirrpocTimi aap;a11i Ha no6yp;oBy.
43. IIOBY,ll;OBA TPHKYTHHKA 3 ,ll;AHHMH CTOPOHAMH
3 a A a 11 a 5.1. H o6yiJysaTU TpUKYTHUIC 3 iJaHUMU CTOpo-
HaMU a, b, c (MaJI. 99, a).
p 0 3 B'H 3 a H H H. 3a ,ll;OilOMOrOIO JiiHiHKH npOBO,IJ;HMO ,ZJ;O- BiJibHY npHMY i noaHa11aeMo Ha Hiii p;oBiJILHy TO'IKYB (MaJI. 99, 6). PoaxHJIOM ~HPKYJIH, m,o p;opiBHIOe a, onHcyeMo KOJIO a ~eHTpoM B i pa,ZJ;iycoM a. Hexaii C - TO'IKanepeTHHY ~boro KOJia a npHMoIO. Tenep poaxHJIOM ~PKYJIH, m,o .zi;opiBHI06 c, onHcyeMo KOJIO a ~eHTpOM y TO'I~ B, a poaxHJIOM ~HPKYmi, m,o
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MaJJ. 99
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AOPiBHIOe b, onHcyeMo KOJIO a u;eHTPOM y To11aj C. Hexaii A -
TO'IKanepeTHHY u;Hx KiJI. IlpoBeAeMo BiApiaKH AB i AC. TpHKYTHHK ABC Mae cTopoHH, md AOPiBHIOIOTb a, b, c.
44. IIOBY,lJ;OBA KYTA, IIJ;O ,Il;OPIBHI06 MHOMY
3 a A a 11 a |
5.2. BiiJxnacTu BiiJ iJauoi niBnpaMoi B iJauy niBnao- |
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UfUHY KyT, UfO iJopiaHJOe iJaHOMY KyTy. |
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p 0 3 u'SI 3 a H H SI. |
IlpoBeAeMO AOBiJibHe KOJIO 3 |
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uepmHHi A ,ZJ;aHoro KYTa (MaJI. 100, a). Hexaii Bi C - |
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cTopoHaMH KyTa. Ilpoue,ZJ;eMo KOJIO pa,ZJ;iycoM AB |
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TO'laj 0 - IlO'laTKOBiH TO'laj ,ZJ;aHOl |
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nepeTHHY u;&oro KOJia a ,ZJ;aHOIO niunpSIMOIO |
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noaHa11HMO B,. OnHmeMo KOJio a u;eHTpoM B, i pa,ZJ;iycoM BC. To11Ka cI nepeTHHY no6y,ZJ;OBaHHX KiJI y ,ZJ;aHiH niBIIJIOID;HHi Jie:lKHTb Ha CTOpOHi myKaHoro KyTa.
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MaJI. 100
;r:J;JISI ,ZJ;OBe,ZJ;eHHSI ,ZJ;OCHTb noKaaaTH, w;o TPHKYTHHKH ABC i OB1C1 piBHi SIK TpHKYTHHKH a ui,ZJ;noBiAHO piBHHMH cTopoHaMH. KyTH
A i 0 e Bi,ZJ;nouiAHHMH KyTaMH D;HX TpHKYTHHKiB.
45. IIOBY,Il;OBA BICEKTPHCH KYTA
3 a A a 11 a 5.3. Ho6yiJyBaTu 6iceKTpucy iJanozo KyTa.
Po au'SI a a H HSI. 3 uepmHHH A ,ZJ;aHoro KyTa SIK a u;eHTpa, onHcyeMo KOJIO ,ZJ;OBiJI&Horo pa,ZJ;iyca (MaJI. 101). Hexaii B i C -
TO'IKHnepeTHHY D;bOro KOJia ia CTOpoHaMH KYTa. 3 TO'IOKB i c THM