Геометрия7_9
.pdf7 KJiac |
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caMHM pap;iycoM onHcyeMo KoJia. Hexau |
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D - TO'IKa ix nepeTHHY, Bi,ll;MiHHa sip; |
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A . IIposep;eMO niBnpRMY AD. |
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IIpoMiHL AD e 6iceKTpHco10, 60 |
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,ll;iJIHTL KYT BAC nonoJiaM. I.J;e BHilJIHBaG |
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3 piBHOCTi TpHKYTHHKiB ABD i ACD, |
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y RKHX KYTH DAB i DAC e sip;nosi,11;- |
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Man. 101 |
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46. AIJIEHH.H BIAPl3KA IlOilOJIAM
3 a A a q a 5.4. HoiJiir.uru eiiJpi3o1' no-
noir.a.11&.
P 03 s'a 3 a H HR. Hexau AB - p;aHHH si,ll;pi3oK (MaJI. 102). 3 TO'IOKA i B pap;iycoM AB onHcyeMo KOJia. Hexan C i C 1 - TO'IKH nepeTHHY ~Hx Kin. BoHH JiemaTL y piaHHX niBilJIOn:µIHax Bi)l;HOCHO IIPRMOl
AB. Bi,ll;piaoK CC 1 nepeTHHae rrpHMy AB y ,n;eRKiH TO'I~ 0. u;a TO'IKai 6 cepep;HHa si)l;piaKa AB.
Cnpasp;i, TPHKYTHHKH CAC 1 i CBC 1 piBHi 38 TpeTLOIO 03H8KOIO piBHOCTi TpH-
Man. 102 KYTHHKiB. 3Bi)l;CH BHilJIHB86 piBHiCTL KYTiB ACO i BCO. TpHKyTHHKH ACO i BCO piBHi 3a rrepmo10 03HaKoIO piBHOCTi TPHKYTHHKiB. CTopoHH AO i BO ~x
TPHKYTHHKiB e si,11;rrosi,11;HHMH, a TOMY soHH piBHi. TaKHM 'IHHOM,
0 - cepe,n;HHa si,n;piaKa AB.
47. IlOBYAOBA IlEPilEH,l\HKYJl.HPHOI IlP.HMOI
3 a ,n; a 11 a 5.5. qe-pea iJa.Hy ro11.1Cy 0 npoeecru npAMy, nepneHiJu1Cyir.sipHy iJo iJa.Hoi npAMoi a.
Po 3 s'a 3 a H Ha. Mom;msi p;sa uuna,11;KH:
1)TO'IKa0 Jie:>KHTL Ha npaMiH a;
2)TO'IKa0 He Jie:>KHTL Ha npaMiH a. PoormrneMo nepmH:H BHnap;oK (MaJI. 103).
§ 5. reoMeTJ)H'IHino6y,AOBH |
71 |
0
B
A |
8 |
a |
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Man. 103 |
Man. 104 |
3 TO'lKH0 AOBiJibHHM paAiYCOM npOBOAHMO KOJIO. BOHO nepeTHe npSIMY a y ABOX T011Kax: A i B. 3 TO'IOKA i B npoBOAHMO KOJia paAiycoM AB. Hexaii C - To11Ka 1x nepeTHHy. lliyKaua npSIMa npoXOAHTb 11epe3 TO'IKH0 i c.
IIepneHAHKYJISlpHiCTL npSIMHX oC i AB eun;rueae a pieuocTi KyTie npu eepmuui 0 TPHKYTHHKiB ACO i BCO. W TPHKYTHHKH piBHi aa TpeTbOIO 03HaKOIO pieHOCTi TpHKYTHHKie.
PoorJISIHeMo APYruii eunaJJ;oK (MaJI.
3 TO'IKH0 npoBOAHMO KOJIO, ~o nepeTHHae npSIMY a. Hexaii A i B - TO'IKHnepeTHHY iioro a npSIMOIO a. 3 TO'IOKA i B TUM caMHM paAiycoM npoeOAHMO KOJia. Hexaii 01 - T011Ka 1x nepeTHHy, ~o JieatHTb y nienJIO~Hi, BiAMiHHiii ei)J; Tie!, y SIKiii JieatHTb T011Ka 0.
IliyKaHa npSIMa npOXOAffTb 11epea TO'IKH0 i 01 .
,D;oee,neMO ~e. 1Ioaua11HMO 11epea c TO'IKY nepeTHHY npSIMHX
AB i 001. TpHKYTHHKH AOB i A01B pieui aa TpeTLOIO oouaKoIO pieuocTi TPHKYTHHKie. ToMy KYT OAC ,nopieu10e KYTY 01AC. ToAi TPHKYTHHKH OAC i 01AC pieHi aa nepm010 oauaKOIO pieHocTi TPHKYTHHKie. 0Tme, 1x KYTH ACO i AC01 pieui. OcKiJILKH qi KYTH cyMimHi, TO eoau npSIMi. TaKuM 'IHHOM, OC - nepneHJJ;HKYJISip, ony~eHHH 3 TO'IKH0 Ha npSIMY a.
48. rEOMETPH'lllEMIC~ Toqox
0,ZJ;HHM 3 MeTOAiB poae'SlayeaHHSI3a):\a11 Ha llOOYAOBY e MeTOA reoMeTpH11HHX MiC~b.
I'eoMerpu'l.HUM MicqeM ro'l.OIC aaaueaeTLCSI cl>irypa, ~o C.KJiaAa6TbCSI 3 ycix TO'IOKIlJIO~HHH, SIKi MaIOTb neeay BJiaCTHBiCTb.
7 KJI8C |
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72 |
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Hanp1uu1a,u;, KOJIO MO»tHa ooHa'IHTHaK |
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I'OOMeTpH'IHeMic~e TO'IOK, piBHOBi,u;,ZJ;aJie- |
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HHX Bi.A ,ZJ;aHOl TO'IKH. |
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Ba»tJIHBe reoMeTpH11He Mic~e TO'IOK,u;ae |
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TaKa TOOpeMa. |
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T e o p e M a |
5.3. I'e0Merpu11.ne |
Micife |
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TO'WJC, pisnosi88aMnux t1i8 8sox 8anux |
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ro11.orc, e npaJIUI., RJCa nepnen8urcyJiapna 80 |
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B t1wpi31C4, |
UfO |
cn0Jiy11.ae l.fi ro11.1eu |
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npo- |
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xo8UTb upe3 ii.ozo |
cepe8uny. |
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Man. 105 |
A o B e A e H H a. |
HexaH: A i B - |
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,u;aHi |
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TO'IKH, a - |
npaMa, |
~o npoxo,AHTb 11epea |
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cepe,ZJ;HHY 0 Bi.ApiaKR AB nepneH,ZJ;HKyJiapHo ,ZJ;O HbOro (MaJI. |
105). |
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MH noBHHHi ,u;oBecTH, ~o: |
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1) |
KO»tHa |
T011Ka |
npaMoi'a piBHOBi,u;,ZJ;aJieHa Bi,ZJ; TO'IOKA |
i |
B; |
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2) |
KO»tHa |
To11Ka D nJio~HHH, piBHoBip;,ZJ;aJieHa Bi,ZJ; TO'IOKA i |
B, |
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Jie»tHTb Ha npHMiH a.
Te, ~o Komua T011Ka C npsMoi'a aHaxo,u;HTbCH Ha op;HaKoBiH Bi,D;CT8Hi Bi,D; TO'IOKA i B, BHilJIHBa6 3 piBHOCTi TPHKYTHHKiB AOC i BOC. Y ~x TPHKYTHHKiB KYTH npH BePWHHi 0 npHMi, CTOpoHa OC cniJibHa, a AO= OB, 60 0 - cepe,u;HHa Bi.ApiaKa AB.
IloKameMo Tenep, ~o KO»tHa TO'IKRD nJIO~HH, piBHOBiMaJieHa Bi,u; TO'IOKA i B, Jie»tHTb Ha npsMiii a. PoarJiaHeMo TPHKYTHHK
ADB. BiH piBHo6e,u;peHHii, 60 AD = BD. Y HbOMY DO - Me,D;iaHa. 3a BJiacTHBicTIO piBHo6e,u;peHoro TPHKYTHHKa Me,u;iaHa, npoBe,ZJ;eHa AO OCHOBH, 6 BHCOTOIO. Orme, TO'IKaD Jie»tHTL Ha IIpHMIB a. Teope~
MY ,u;oBe,u;eHo.
49. METO,ll, rEOMFI'PH'IHHX MICD;b
PoarJIHHeMo cyTL MeTO,ZJ;Y reoMeTpH'IHHXMic~b, HKHii BHKOpHCToByeTLCH y npo~eci poaB'aayBaHHSIaa,u;a11 Ha no6y,u;oBy. Hexaii, ~o6 poas'saaTHaa,Aa11y Ha no6y,u;osy, HaM noTpi6Ho aHaiiTH HKYCb
~O 3a,D;OBOJibHH6 ,D;Bi YMOBH. reoMeTpH'IHeMic~e TO'IOK,
~o aa,u;oBOJibHHIOTb nepmy yMoBy, s ,u;eaKa «Pirypa Fi, a reoMeTpH11He Mic~e TO'IOK,~o 3a,D;OBOJILHHIOTL ,u;pyry YMOBy, 6 ,ZJ;eHKa «l>irypa
F2. illyKaHa TO'IKaX HaJie»tHTL Fi i F2, To6To e ix TO'IKOIOnepeTHHy. HK~o ~i reoMeTpH'IHiMic~s npocTi (cKamiMo, cKJia,u;aIOTLCH 3 IIpHMHX i KiJI), TO MO»tHa i'xno6y,ZJ;yBaTH i 3HaiiTH TO'IKYx, HKa Hae ~iKaBHTL. HaBe,u;eMo npHKJia,u;.
§ 5. reoMeTpmlHi IIOOy,D;OBH |
73 |
MaJI. 106
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•
3 a A a q a (43). ,ll;aHo TPH TO'IKH A, |
B, C. |
Ilo6YAYHTe |
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TO'IKYX, .RKa OAHaKoao aiAAaJieHa BiA TO'IOKA |
i Bi aHaxo- |
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AHTbC.R Ha AaHi:H BiACTaHi BiA TO'IKHc. |
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p 0 3 a'g |
3 a H H .R. lllyKaHa TO'IKa x |
3aAOBOJibH.R6 ABi |
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yMoau: 1) |
OAHaKoao BiAAaJieHa ai.A TO'IOKA i B; 2) JiemHTb |
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Ha AaHiii BiACTaHi BiA TO'IKHC. reoMeTpH'IHeMic:a;e TO'IOK,Ill;O 3aAOBOJlbH.RIOTb nepmy YMOBy, 6 np.RMa, .RKa nepneHAHKYJI.RpHa AO BiApiaKa AB i npoXOAHTb qepea :Horo cepeAHHY (MaJI.
106). reoMeTpH'IHeMic:a;e TO'IOK,Ill;O 3aAOBOJibH.RIOTb Apyry YMOBy, 6 KOJIO ,n;aHoro paAiyca 3 :a;eHTpOM y TO'l:a;ic. lllyKaHa TO'IKa x JiemHTb Ha nepeTHHi D;HX reoMeTpH'IHHX Mic:a;b.
KOHTPO~bHI3AllHTAHH.H
1.I.IJ;o TaKe KOJIO, :a;eHTP KOJia, paAiyc?
2.I.IJ;o TaKe XOpAa KOJia? HKa XOpAa Ha3HBa6TbC.R AiaMeTpOM?
3.HKe KOJIO HaauaaeTbC.R onucaHHM HaBKOJio TpHKYTHHKa?
4.,ll;oBeAiTb, w;o :a;eHTP KOJia, onucaHoro HaBKOJIO TPHKYTHHKa, JiemHTb Ha nepeTHHi cepeAHHHHX nepneHAHKYJI.RpiB AO cropiH
TpHKYTHHKa.
5. .HKa np.RMa Ha3HBa6TbC.R AOTH'IHOIOAO KOJia?
6. I.IJ;o 03Ha'la6:KOJia AOTHKaIOTbC.R B AaHiH TO'l:a;i?
7. .HKHH AOTHK KiJI Ha3HBa6TbC.R 30BHimHiM, .RKHH - BHyTpimHiM?
8.HKe KOJIO Ha3HBa6TbC.R anucaHHM y TPHKYTHHK?
9.,ll;oBeAiTb, w;o :a;eHTP KOJia, BITHCaHoro y TPHKYTHHK, JiemHTb Ha nepeTHHi :Horo 6iceKTpHc.
7 KJiac |
74 |
10.IIoscaiTL, SK no6YAYBaTH TPHKYTHHK aa TPLOMa cTOpoHaMH.
11.Ilo.HCHiTh, .HK Bi)J;KJiaCTH Bi)!; )J;attoi: niBIIpRMOl y )J;aHy rriBIIJIOID;HHY KyT, w;o AOPiBHIOe AaHoMy KyTy.
12.IIoscHiTL, SK no,u;iJIHTH ,u;aHHH KYT nonoJiaM.
13.IIoscHiTL, SIK rro)J;iJIHTH ,D;aHHH Bi)J;piaoK IIOIIOJiaM.
14.IIo.HcHiTh, .HK qepea ,D;aHy TO'IKYrrpoBeCTH rrpsMy, rreprrett)J;HKYJISPHY AO )J;aHOl rrpSMOl.
15.I.U;o SIBJISl6 co6010 reoMeTpH'IHeMiCl\e TO'IOK,piBHOBiAAaJieHHX BiA ABOX AaHHX TO'IOK?
• 3A,]µ.'11
1. AoBeAiTL, w;o 6y,u;L-aKHH npoMiHL, SKHH BHXOAHTL 3 l\eHTpa KOJia, nepeTHHae KOJIO B OAHiH TO'laj.
2. AoBeAiTL, w;o npaMa, sKa npoXOAHTL qepea l\eRTP KOJia, nepe-
THHae KOJIO y ABOX TO'llUlX.
3. AoBeAiTL, w;o AiaMeTp KoJia, SIKHH rrpoxo)J;HTL qepea cepe)J;HHY
XOPAH, neprreHAHKynspHHH AO ael.
4. Cq>0pMyJI10iiTe i p;oBe)J;iTL TeOpeMy, o6epaeHy )J;O TBepAmeHHSI aa,u;a'li3.
5. 1) 3 TO'IKHp;attoro Kona npoBe,u;etto )J;iaMeTp i xop,u;y, w;o )J;opiBHIOe paAiycy. 3Haii,u;iTL KYT MilK HHMH (MaJI.
2) 3 TO'IKH)J;aHoro KOJia rrpoBep;eHO )!;Bi xop)J;H, w;o )J;OpiBHIOIOTh pap;iycy. 3Haii,u;iTL KYT Mim HHMH.
6. AoBe)J;iTL, w;o cepe,u;HHHi rreprreH,u;HKYJISIPH )J;O )!;BOX cTopiH TpH-
KYTHHKa nepeTHHaIOTLCSI.
7. 1lH MO:>Ke KOJIO )J;OTHKaTHCS ,Zl;O IIpSIMOl y )!;BOX TO'!Kax?IIosc-
HiTL Bi)J;IlOBi)l;L. |
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8. AoBe)l;iTL, w;o p;oTH'IHa)J;o KOJia ae |
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Mae 3 HHM iHWHX cniJILHHX TO'IOK, |
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KpiM TO'IKH)J;OTHKy. |
1----...-----•A |
9. HKi KYTH yTBopioe xop)J;a AB, w;o |
p;opiBHI06 pa,11;iycy KOJia, 3 )J;OTH'IHOIO |
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B TO'lajA? |
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10. 3HaHAiTL KYTH, ni)J; SIKHMH nepeTH- |
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HaIOTLCS rrpSIMi, w;o )l;OTHKaIOTLCSI |
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AO KOJia B KiHJ:J;SIX XOp)J;H, SIKa )J;OpiB- |
MaJI. 107 |
HI06 pa)J;iycy. |
§ 5 . reoMeTpH'IHi no6y,a;OBH |
75 |
11.Kona a pap;iycaMH 30 CM i 40 CM p;oTHKaIOTLC.s:. 3Haii.u;iTL Bi.u;- CTaHb Mim u;eHTpaMH Kin y BHIIap;Kax 30BHllnHbOro i BHyTpimHboro ,D;OTHKiB.
12.1IH MOatYTb AOTHKRTHC.S: ABa Kona, .S:KID;O 'ixpaAiYCH AOPiBHIOIOTb 25 CM i 50 CM, a BiACTRHb Mim u;eHTpaMH 60 CM?
To11KH A, B, C nemaTb Ha np.s:Miii, a T011Ka 0 - noaa np.s:- MOIO. 1IH MomyTb p;Ba TPHKYTHHKH AOB i BOC 6yTH piBHo6e,zi;- peHHMH a ocHoBaMH AB i BC? IIo.s:cHiTb Bi.u;noBip;b.
2) 1IH MOatYTb Kono i np.s:Ma nepeTHHaTHC.S: 6inbme, Him y ABOX TO'IKax?
14!' 1) Kona a u;eHTpaMH 0 i 01 nepeTHHaIOTLC.S: B To11Kax A i B.
,D;oBep;iTb, w;o np.s:Ma AB nepneHp;HKyn.s:pHa .u;o np.s:Mo'i001.
2) ,D;oBe.u;iTb, w;o .u;sa KOJia He MOatYTb nepeTHHaTHC.S: 6iJibWe, Him y ABOX TO'IKax.
15!' 1) 1Iepea TO'IKYA KOJia a u;eHTPOM 0 npoBeAeHo np.s:My, w;o He
.u;oTHKaeTbC.S: AO KOJia OB - nepneHAHKYn.s:p, onyw;eHHii Ha np.s:My. Ha npoAOBateHHi Bip;piaKa AB BiJJ;Kna,ll;eHo Bi.u;piaoK
BC= AB. ,D;oBe,ll;iTb, w;o T011Ka C nea<HTb Ha KOJii.
2),D;oBeAiTb, w;o KOJIH np.s:Ma Mae 3 KOnOM TinbKH OJJ;HY cniJibHY TO'IKY, TO BOHa 6 JJ;OTH'IHOIO/1,0 Kona B u;iii TO'lu;i.
3),D;oBep;iTb, w;o KOJIH ABa KOJia MRIOTb TiJibKH OJJ;HY cniJibHY TO'IKY,TO BOHH AOTHKalOTbC.S: B u;iii TO'lu;i.
16!' 1) 3 OAHiei TO'IKHAO KOJia npoBeAeHO ABi AOTH'IHi(Man. 108).
,D;ose/1,iTb, w;o BiApiaKH AOTH'IHHxMP i MQ piBHi.
2) ,D;oBeAiTb, w;o 11epea OAHY TO':lKyHe Mome npoXO,ll;HTH 6iJibWe
ABOX AOTH'IHHXAO KOna.
17.0AHe Kono OIIHCaHe HRBKOJIO piBHOC'l'OpOHHbOroTPHKYTHHKa, a APYre - BIIHCaHe B H1>oro. ,D;oBeAiTb, w;o u;eHTPH D;HX KiJI a6iraIOTLCH.
[
Man. 108 |
Man. 109 |
7 KJIRC |
76 |
18. KoJio, BilHCaHe y |
TpHKYTHHK ABC, AOTHKa6TLCSI AO iioro |
cTopiH y TO'IKaXAi. B1, C1 (MaJI. 109). ,ZJ;oBeAiTL, m;o AC1 =
-AB+ AC-BC
2
19. Ilo6YAYHTe TPHKYTHHK 3a TPLOMa CTOpOHaMH a, b i c, SIKlll;O: 1) a= 2 CM, b = 3 CM, c = 4 CM; 2) a= 3 CM, b = 4 CM, c = = 5 CM; 3) a = 4 CM, b = 5 CM, C = 6 CM.
20.,ZJ;aHo TpHKYTHHK ABC. Ilo6YAYHTe iHmHii TPHKYTHHK ABD, m;o AOPiBHI06 HOMY.
21.Ilo6YAYHTe KOJIO AaHoro paAiyca, m;o npOXOAHTh qepe3 ABi AaHi
TO'IKH.
22.Ilo6YAYHTe TpHKYTHHK 3a ABOMa CTOPOHaMH i paAiycoM onHcaHoro KoJia.
23.Ilo6yAyiiTe TpHKYTHHK ABC 3a TaKHMH AaHHMH:
1)3a ABOMa CTOpOHaMH i KYTOM Mim HHMH:
a) AB= 5cM, |
AC= 6cM, |
LA= 40°; |
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6) |
AB = 3 CM, |
BC = 5 CM, |
L B = 70°; |
2) |
3a CTOPOHOIO i npHJierJIHMH AO Hei'KyTaMH! |
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a) |
AB= 6 cM, |
LA= 30°, |
LB= 50°; |
6) |
AB= 4cM, |
LA= 45°, |
LB= 60°. |
24.Ilo6yAyHTe TpHKYTHHK 3a ABOMa CTOpOHaMH i KYTOM, npOTHJieJKHHM 6iJILmiH 3 HHX:
a) a= 6 CM, |
b = |
4 CM, |
a= 70°; |
6) a= 4 CM, |
b = |
6 CM, |
p = 100°. |
25.Ilo6YAYHTe piBHo6eApeHHH TpHKYTHHK 3a 6i'IHOIOCTOPOHOIO i KYTOM npH OCHOBi.
26.Ilo6YAYHTe KOJIO, BilHCaHe B AaHHH TPHKYTHHK.
27.IloAiJiiTh KYT Ha 'IOTHPHpiBHi 'IaCTHHH.
28.Il06YAYHTe KYTH 60° i 30°.
29.,ZJ;aHO TpHKYTHHK. Ilo6YAYHTe H:oro MeAiaHH.
30.Ilo6YAYHTe TpHKYTHHK 3a ABOMa CTOpoHaMH i MeAiaHOIO, npoBeAeHOIO AO OAHiei'3 HHX.
31.Ilo6YAYHTe TpHKYTHHK 3a CTOPOHOIO, MeAiaHOIO, npoBeAeHOIO AO ~iei' CTOpOHH, i paAiyCOM onucaHoro KOJia.
32.Ilo6YAYHTe TpHKYTHHK 3a ABOMa CTOpoHaMH i MeAiaHOIO, npoueAeHOIO AO TpeThOl CTOpoHH (MaJI. 110).
33.,ZJ;aHO TPHKYTHHK. Ilo6YAYHTe iioro BHCOTH.
34.Ilo6YAYHTe KOJIO, OilHCaHe HaBKOJIO AaHoro TpHKYTHHKa.
§ 5. reoMeTpmrni rro6yAOBH |
77 |
Man. 110
35.IIo6yp;yiiTe npSIMOKYTHHii TPHKYTHHK aa rinoTeHyaoro i KaTeTOM.
36.IIo6yp;yiiTe pisHo6ep;peHHii TPHKYTHHK aa 6i•rnoro cTopoHoro i BHCOTOIO, onym;eHOIO Ha OCHOBY.
37.IIo6yp;yiiTe TPHKYTHHK aa ABOMa CTOPOHRMH i BHCOTOIO, orryw;e- HOIO Ha TpeTIO CTOpoHy.
38.IIo6yp;yiiTe TPHKYTHHK aa ABOMa cTopoHaMH i BHCOTOIO, orryw;e- HOIO Ha OAHY 3 HHX.
39.IIo6yp;yiiTe TpHKYTHHK aa cTopoHOIO i rrposep;eHHMH p;o Hei Mep;iaHOIO Ta BHCOTOIO.
40.IIo6yp;yiiTe piBH06ep;peHHii TPHKYTHHK aa ocHosoro i pap;iycoM OilHCaHoro KOJia.
41.,D;ose)J;iTb, w;o reoMeTpH'IHeMic~e TO'IOK,Bip;p;aJieHHX BiA p;aHoi IIpSIMOl Ha Bi)J;CTaHb h, CKJIRAR6TbCSI 3 ));BOX IlpSIMHX, rrapaJieJib- !IHX p;aHiii i Bip;p;aJieHHX sip; Hei Ha h.
42.Ha p;aHiii npSIMiii aHaiip;iTI> TO'IKy,.RKa aHaxop;HTbCSI Ha p;aHiii BiACTRHi BiA p;pyroi p;aHoi rrp.RMOl.
43.,D;aHo TPH TO'IKH:A, B, C. IIo6yp;yiiTe TO'IKYX, SIKa op;HaKoBo sip;p;aJieHa sip; TO'IOKA i B i aHaxop;HTI>CSI Ha p;S:Hiit sip;cTaHi Bip; TO'IKHC.
44.Ha p;aHiii npS1Miii aHaiip;iTI> TO'IKy,piBHOBip;p;aJieHy sip; p;sox )J;RHHX TO'IOK.
45.,D;aHo 'IOTHPHTO'IKH:A, B, C, D. 3Haiip;iTI> TO'IKYX, S1Ka op;Ha-
KOBO sim~aJieHa sip; TO'IOKA |
i B i op;HaKoBo sip;p;aJieHa sip; |
TO'IOKc i D. |
• |
46?" IIo6yµ;yiiTe TPHKYTHHK, SIKIIl;O ));RHO CTOpOHy, rrpHJierJIHH AO Hei KYT i CYMY ,ll;BOX iHmHX CTOpiH (MaJI.
7 KJIBC |
78 |
Man. 111
47'!'Ilo6YAYHTe TpHKyTHHK, .RKID;O AQHO CTOpoHy, npHJierJIHH AO Hei
KYT i pi3HHD;l0 ABOX iHWHX CTOpiH.
48'!'Ilo6YAYHTe npHMoKyTHHH TPHKYTHHK aa KaTeToM i cyMOIO p;pyroro KaTeTa :H rinoTeHyaH.
49'!'l) 3 TO'IKHA p;o KOJia a n;eHTPOM 0 i pap;iycoM R npoBep;eHo ,D;OTINHY (MaJI. ,lJ;oBep;iT&, m;o TO'IKaC AOTHKY JiemHTb Ha OCHOBi piBH06ep;peHoro TpHKYTHHKa OAB, y SIKoro OA = AB, OB= 2R.
2) IIpoBep;iT& p;oTH'IHYp;o KoJia, .RKa npoxop;HT& 11epea p;aHy TO'IKYnoaa KOJIOM.
50'!'IIpoaep;iT& cniJI&Hy ,D;OTH'IHYp;o p;Box p;aHHX KiJI (MaJI. 113).
B
Man. 112 |
Man. 113 |
8KJiac
§6. 'IOTHPHKYTHHKH
50.03HAqEHH.H qoTHPHKYTHHKA
lfOTUPU1CYTHUKOM Ha3HBa6TbCH <l>irypa, HKa CKJia,D;a6TbCH 3 qQTHpbOX ToqoK i qQTHpbOX Bi,D;piaKiB, w;o IIOCJii,D;OBHO 'ixCIIOJiyqa - IOTb. IlpH D;bOMY JKO,D;Hi TpH 3 ,D;aHHX ToqoK He IIOBHHHi JieJKaTH Ha O,D;HiH rrpn:Mi:H, a Bi,D;piaKH, HKi 'ixCIIOJiyqaIOTb, He IIOBHHHi rrepeTHHaTHCb. ,lJ;aHi TOqKH Ha3HBaIOTbCH 6epULUHaMU qoTHpHKYTHHKa, a Bi,D;pi3KH, w;o 'ix CIIOJiyqaIOTb,- CTOPOHaMU qQTHPHKYTHHKa.
3 a ,D; a q a (1). Ha MaJIIOHKax 114-116 ao6pameHo TPH <l>irypH, KOJKHa 3 HKHX CKJia,D;a6TbCH 3 qoTHpbOX ToqoK i qQTHpbOX Bi,D;piaKiB, HKi IIOCJii,D;OBHO 'ixCIIOJiyqaIOTb. .HKa 3 D;HX <l>iryp 6 qQTHpHKYTHHKOM?
p 0 3 B'H 3 a H H H. l:JOTHPHKYTHHKOM 6 JIHWe <l>irypa Ha MaJIIOHKY 116, 60 y <l>irypH Ha MaJIIOHKY 114
JieJKaTb Ha O,ll;HIB rrpHMIB, a y <l>irypH Ha MaJIIOHKY 115 Bi,D;piaKH BC i AD rrepeTHHaIOTbCH.
BepmHHH qoTHpHKYTHHKa Ha3HBaIOTbCH cyciiJniMu, HKIIl;O BOHH s KiHD;HMH o,D;His'ia lioro cTopiH. Hecyci,D;Hi BepmHHH HaaHBaIOTbCH nporu.ne31CHUMU. Bi,D;piaKH, w;o c110Jiyqa10Tb rrpoTHJiemHi BepmHHH qoTHPHKYTHHKa, Ha3HBaIOTbCH iJiazona.nstMU.
y qoTHpHKYTHHKY Ha MaJIIOHKY 11 7 ,D;iaroHaJIHMH 6 Bi,D;pi3KH
AC i BD.
CTopOHH qQTHPHKYTHHKa, w;o BHXO,ll;HTb 3 O,D;Hie'iBepmHHH, Ha3HBaIOTbCH cyciiJHiMu cTopoHaMH. CTopoHH, HKi He MaIOTb crriJibHOro KiHIJ;H, Ha3HBaIOTbCH nporu.ne31CHUMU CTOPOHaMH.
y qoTHpHKYTHHKY Ha MaJIIOHKY 11 7 rrpOTHJieJKHHMH e CTOpOHH
AB i CD, BC i AD.
A D A
MaJI. 114 |
MaJI. 115 |