Геометрия7_9

7 KJiaC

40

[

A	B	B,
		MaJI. 55

Hexaii A1B1C2 - TpHKYTHHK, w;o .a;opiBHI06 TPHKYTHHKY ABC, a BepmHHa iioro C2 JiemHTb B o,o;HiH niBnJIOIIJ;HHi a BepmHHOIO C 1 B~HOCHO npRMo1 A1B1 (MaJI. 55).

Hexa:H D - cepe,o;HHa s~pi3Ka C1C2. TpHKYTHHKH A1C1C2 i B1C1C2 ·- piBHo6eApeHi i3 cniJibHOIO ocHosoro C1C2. ToMy 1x MeAiaHH A 1D i B 1D e BHCOTaMH. To.a;i npRMi A 1D i B 1D nepneH,ll;HKYm1pHi ,o;o npRMo'iC1C2. IIpHMi A1D i B1D He a6iraIOTbCR, ocKiJibKH TO'IKHAi. B1, D He JiemaTb Ha OAHiH npSIMiH. AJie 11epea TO'IKYD npSIMo'iC1C2 MomHa nposecTH JIHme o,o;Hy nepneHAHKYJISIPHY .a;o He'i npSIMY. MH AIBIIlJIH ,o;o cynepe11HocTi. TeopeMy .a;ose,o;eHo.

3a,11;a11a (29). Y _TPHKYTHHKiB	ABC i A1B1C1: AB=
= A1B1, AC= A1Ci. LC= L C1 = 90°.		,ll;oee,o;iTb, w;o
6. ABC= 6. A1B1C1.
Po 3 s'Ra a H HSI. Hexa:H ABC i	A 1B1C 1-	AaHi TPHKYT-

H:KKH (MaJI. 56). 1Io6YAY6MO TpHKYTHHK CBD, w;o ,o;opiBHIOG TPHKYTHHKY CBA, i TpHKYTHHK C1D1B1, w;o ,o;opiBHIOe TpHKYTHHKY C1A1B1.

8 B,

A	[	D	A,	c,	o,

MaJI. 56

§ 3. 03HRKH pillHOCTi TPHKYTHHKill

41

TpeKyTHHKH ABD i A1B1D1 piBHi aa TpeThOIO oaHaKoIO. Y HHX AB= A1Bi. 3a yMOBOIO 3&Aa•li; AD= A1Di. ocKiJihKH

AC= A1C1; BD = B1Di. 'lepe3 Te ~o BD =AB, B1D1 =

= A1B1. 3 piBHoCTi TpHKYTHBKiB ABD i A1B1D1 BHnJIHBas

piBHicTh KyTiB: L A =	L A 1. OcKiJxbKH 3a	yMOBOIO AB =
= A1Bi. AC= A1Ci. a	LA= L A1 38	AOBeAeHHM, To

TPHKYTHHKH ABC i A1B1C1 piBHi 3a nepmo10 03H8KOIO.

28. .HK CAMOCTIHHO rOTYBATHCb 3A Ill,ll,PY'IHHKOM

Mome TpanHTHCJ., ~o 3 ,u;eaKHX npH'IHH, H8IlPHKJiaA 11epea XBOpo6y, BH He 6yJIH Ha ypo~ reoMeTpii. To,u;i M8TepiaJI :u;i.oro ypo-

KY B&M AOBeAe'l'bCSBHB'IHTHcaMocTiiiHo aa niApy'IHHKOM.TeKcT ni,D;py'IHHK8CJii.A 'IHT8TJIHe nocrrimaIO'IH,OKpeMHMH pe'leHHBMH, He uepeXOAHTH AO H8CTYilHOI'O pe11eHHa, He 3po3YMiBWH 3MiCT nouepeAHi.oro. PoarJIHHeMo KOHKpeTHHii rrpHKJia,u; - ,u.oBe,u.eHHSI TpeThOi oaaaKH piBHOCTi TPHKYTHHKiB. 0Tme, 'IHTaeMoTeKCT ni,u.- PY'IHHKa:

•.HK~o TPH CTOPOHH o,u.aoro TpHKYTHHKa AOPiBHIOIOTb Bi,u.noBiA-

HO TphOM CTopoHaM ,u.pyroro TPHKYTHHKa••• •

~o6 3po3yMiTH 3MiCT ~Oro pe'IeHHR,Tpe6a 3HaTH, w;o T&Ke TpHKYTHHK, Aoro cTopoHH i piBHiCTi. cropiH. BH Bee ~e aaaere, TOMY 3Mi.CT rrpo'IHTaHOl'Ope11eHH$1 BRM apoayMiJIHii. qHT86MO ,U.8Jli:

tTO TRKi TpHKYTHHKH piBHh.

~o6 3p03YMiTH 3Mi.CT ~ro pe'IeHHH, rrOTpi6HO 3H8TH, aKi TpmcyTHHKH H&3HB&IOTbCH piBHHMH. A.ne BH i :u;e 3Ha6Te. TaKHM

'IHHOM,3MiCT TeopeMH BaM 3po3yMiJIHH. qHTa6MO AOBeAeHHa.

;lJ;oBe,u.eaaa. •Hexaii ABC i A1B1C1 -,u.Ba	TPHKYTHHKH,
y aKHX AB= A1Bi. AC= A1Ci. BC= B,c, (MaJI.	55). IIoTpi6ao

,11,0BecTH, w;o TpHKYTHHKH piBHh.

TYT Bee apoayMiJio. IloaHa'IaIOTl>caTPHKYTHHKH, HKi 38,11,0BOJihHaIOTh yMoBy reopeMH i piBHiCTb HKHX noTpi6Ho ,u.oBeCTH.

•IIpHilYCTHMO, w;o TpHKYTHHKH He piBHi•.

Bu 68'IHTe,w;o po6HMO npunyw;eHHH, rrpoTBJiemHe TBepAmeHHJO TeOpeMH. OTme, B npo:u;eci no,u.an:i.DIHx MipKyB&Hb MH M86MO npHiiTH 11.0 cynepe'IHOCTi(AOBe,u.eHHa Bi.A cynpoTHBHoro).

•To,u.i y HHX LA =I= L Ai, LB =I= LB,, LC =I= LC 1.

IHaKme BOHH 6yJIH 6 piBHi 38 nepmo10 oaaaKOIO•.

7 KJiac

42

IlpHra,11;aiiTe nepmy oaHaKy piBHOCTi TPHKYTHHKiB. IIepeKoHaii:- TecL y TOMY, m;o KOJIH BHKOHy6TLCS xoqa 6 O)J;Ha 3 piBHOCTeH

LA= L Ai, LB= L Bi, LC= L Ci, TO TPHKYTHHKH ABC i

A1B1C1 pisHi, a u;e cynepeqffT& apo6JieHOMY npHnym;eHHIO. •Hexaii A1B1C2 - TPHKYTHHK, m;o ,11;opiBHI06 TPHKYTHHKY ABC,

i iioro BepmHHa c2 Jie)l(HTL B O,ll;HiH niBilJIOID;HHi 3 BepmHHOIO c I

Bi,ll;HocHo npaMo'iA 1B1 (MaJI. 55)•.

TYT see apooyMiJio. We10 cl>paao10 noqHHaJIOCL ,11;ose,11;eHHH nepmo'ii ,11;pyro'ioaHaK.

•Hexaii D - cepe,IJ;HHa si,ll;pi3Ka C1C2•. BH 3Ha6Te, m;o TaKe cepe,11;HHa si,ll;pi3Ka.

•TpHKYTHHKH A1C1C2 i B1C1C2 - pisHo6e,11;peHi ia cniJILHOIO OCHOBOJO C1C2•.

~o6 3po3yMiTH 3MiCT D;LOl'OTBep,11;meHHS, Il0Tpi6HO 3HaTH, JIKHH TPHKYTHHK Ha3HBa6TLCS piBHo6eApeHHM i JIKa iioro CTOpoHa Ha3HBa6T&CS OCHOBOIO.

•ToMy 'ixMe,11;iaHH A 1D i B1D e BHCOTaMH•.

3MicT o;LOro peqeaaa BaM apooyMiJIHii. BH aaaeTe, m;o TaKe Me,ll;iaHa, BHCOTa, i 3HaeTe BJiaCTHBiCTb Me)J;iaHH piBH06e,ll;peHOl'O TPHKYTHHKa.

•OTme, npBMi A 1D i B1D nepneH,ll;HKyJiapHi ,11;0 npsMol C1C2•. HcHo.

•IlpHMi A1D i B1D He a6iraJOTLCH, ocKiJILKH TO'IKHAi. Bi. D He JiemaTL Ha O,ll;Hiii npHMiiit.

3poayMiJio. HK6H TO'IKaD JiemaJia Ha npaMiii A 1Bi. TO TO'IKH

C 1 i C2 JiemaJIH 6 y piaHHx niBIIJIOID;HHax BiAHOCHo npsMo'iA 1B 1.

•AJie 11epea T011Ky D npBMo'iC1C2 MOmHa nposecTH JIHme OAHY

nepneH,ll;HKYJISPHY ,11;0 He'inpHMY•· Hcao. BH aHaeTe TaKy TeOpeMy.

	•MH npHHmJIH ,11;0 cynepe'IHOCTb.
3pooyMiJIO.
	• TeopeMy ,11;0BeAeHo •.
?	KOHTPO~bHI3AilHTAHHH
•

1.)J;oBeAiTL nepmy oaHaKy pisHocTi TpHKYTHHKiB. HKi aKcioMH BHKOpHCTOBYIOTLCS npH ,ll;OBe,ll;eHHi TOOpeMH 3.1?

2.Ccl>opMyJ110iiTe i ,ll;OBe,ll;iTb Apyry oaHaKy piBHocTi TPHKYTHHKiB.

3.SIKHH TPHKYTHHK Ha3HBaGTLCJI piBHo6e,11;peHHM? SIKi CTOPOHH

§ 3. 0aHaJCH piBHOCTi TPHKYTHBKiB

43

piBHOOeApeHoro TPHKYTHHKa HR3HBRIOTbCSI 6i'IHHMH CTOpo-

HRMH? Hxa CTOpOHa HR3HBR6ThCSI OCHOBOIO?

4.,IJ;oBeAiTb, m;o y piBH06eApeHOMY TPHKYTHHKY KYTH npH OCHOBi piBHi.

5.HKHii TpHKYTHHK Ha3HBR6TbCSI piBHOCTopoHHiM?

6.,IJ;oBeAiTb, m;o KOJIH y TpHKYTHHKY ,D;Ba KYTH piBHi, TO BiH piBHOOe,Z\peHHH.

7.IloSicHiTb, m;o TaRe o6epHeHa TeopeMa. Haue,ll;iTb npHKJiaA. 1IH )'.\JI$lKOlRHOl TeopeMH npaBHJibH8 o6epHeHa?

8.~o T&Ke BHCOTa TPHKYTHHK8?

9.~o T&Ke 6icexTpHC8 TPHKYTHHK8?

10. ~o TaKe Me,ll;iaaa TpHKYTHHK8?

11.,D;ose,ll;iTb, m;o y pisuo6eApeHoMy TPHKYTHHKY Me,ZJ;iaHa, npose- ,ZJ;eaa ,Zl;O OCHOBH, e BHCOTOIO i 6iceKTpHCOIO.

12.,IJ;oae,ll;iTb TPeTIO oaHaKy piBHocTi TPHKYTHHKiB•

• 3A~'II

1. BiApiaxH AB i CD nepeTHHaIOTbC.H B ro11~ 0, SIKa e cepeAHHOIO KO>KHoro a uux. 1IoMy ,D;opiBHI06 ui,l\piaox BD, HKID;O AC=

= 10M?

2. 1Iepea cepe,ZJ;HHy 0 Bi,l\piaKa AB npoBe,D;eHo npSIMY, nepneHAHKYJI.HPHY AO np.HMoi AB (MaJI. 57). ,IJ;oue,ll;iTb, m;o KOlRHa TO'IKa~iei np.HMoi O.Z\H&KOBO Bi.l\A&JieHa um TO'IOKA i B.

3. Ha cTopoHi AB TPHKYTHHKa ABC B3HTo TO'IKYD, a ua cTopoui

A1B1 TPHKYTHHKaA1B1C1 - T011Ky D1. Bi,l\oMo, m;o TPHKYTHHKH ADC i A1D1C1 piBHi ii Bi,D;piaKH DBi D1B1 piBHi. ,IJ;oue,ll;iTb piBHicTb TPHKYTHHKiB ABC i A1B1C1:

A

0

B

£

D

MaJI. 57

MaJI. 58

= BD.

7 Knac

44

4.ID;o6 BHMip$1TH Ha Micu;eBOCTi Bi,ll;CTaHb Mim ,ll;BOMa TO'IKaMH

A i B, Mim 8KHMH He MOmHa npoiiTH no np8Miii (MaJI. 58), BH6HpaIOTb TaKy TO'IKYc, 3 $1KOl MO)KHa npoHTH ,11;0 TO'IKHA i ,11;0

	TO'IKHBi a 8Koi BH,n;Ho o6H,n;Bi u;i TO'IKH.IlpoBiwyIOTL 1Bi,n;cTa-
	Hi AC i BC, npo,n;oBmyIOTb ix aa TO'IKYC i Bi,ll;KJia,n;a10T1> CD =
	= AC i EC= CB. To,n;i Bi,n;piaoK ED ,n;opiBHIOe wyKaHiH Bi,n;-
	cTaHi. Il0$1CHiTb 'IOMy.
5.	Bi,ll;piaKH AB i CD nepeTHHaIOTbC$1 B TO'lu;i0 (MaJI. 59). ,ll;oBe-
	,n;iTL piBHiCTb TPHKYTHHKiB ACO i DBO, KOJIH Bi,n;oMo, w;o KYT
	ACO ,n;opiBHI06 KYTY DBO i BO= CO.
6.	Bi,n;piaKH AC i BD nepeTHHaIOTLC$1 B TO'ID;i0 (MaJI. 60). ,ll;oBe-
	,n;iTh piBHiCTb TpHKYTHHKiB BAO i DCO, KOJIH Bi,n;oMo, w;o KYT
	BAO ,11;opiBHI06 KYTY DCO i AO = CO.

7"!',ll;oBe,ll;iTb piBHiCTb TPHKYTHHKiB aa Me,11;iaHOIO i KyTaMH, Ha $1Ki BOHa poa6HBa6 KYT TpHKYTHHKa.

8.ID;o6 BHMip8TH Ha Micu;eBOCTi Bi,ll;CTaHb Mim ,ll;BOMa TO'IKaMHA i

B, a $1KHX o,11;Ha (To'IKaA) HenpHcTynHa, npoBiwyIOTb Hanp8M Bi,ll;piaKa AB (MaJI. 61) Ta Ha :Horo npo,11;0BmeHHi Bi,n;KJia,n;aIOTb

,n;oBiJihHHH Bi,ll;piaoK BE. B116Hpa10T1> Ha Micu;eBocTi TO'IKYD,

a 8Koi BH,ll;HO TO'IKYA	i MO»eHa npoiiTH ,n;o TO'IOKBi E. Ilpo-
. Biwy10T1> np8Mi BDQ i	EDF i BHMip1010T1> FD = DE i DQ =

,ll;ani ii,11;yT1> ya,n;oBm np8Moi FQ, ,ll;HB1l$1'1HCbHa TO'IKY

A, noKH He aHaii,n;yT1> TaKy TO'IKYH, 8Ka JiemHTb Ha np8MiH AD.

To,n;i HQ ,n;opiBHIOe wyKaHiH Bi,ll;cTaHi. ,ll;oBe,n;iTL u;e.

9.IlepHMeTp (cyMa ,ll;OB»CHH CTOpiH) piBH06e,n;peHoro TpHKYTHHKa ,n;opiBHIOE: 1 M, a OCHOBa 0,4 M. 3Haii,n;iTb ,ll;OB)KHHY 6i'IHOl CTOpOHH.

A	D A	0
Man. 59		Man. 60

1 HanpRM BHaHa'laJOT&*ep,ll;HH&MH-eixaMH.

§ 3. 03H8KH piBHOCTi TpHKyTHHKiB

45

B

MaJI. 61

MaJI. 62

10.IlepuMeTp pi:eH06eApeHoro TPHKYTHHKa AOPiBHI06 7,5 M, a 6i11Ha CTOpoHa AOPiBHIOG 2 M. 3HaiiAiTL OCHOBy.

11.IlepuMeTp piBHo6eApeHoro TPHKYTHHKa AOPiBHIOe 15,6 M. 3HaHAiTL HOI'O CTOPOHH, $1K~o: ·1) OCHOBa MeHIIla aa 6i11Hy CTOpoHy Ha 3M; 2) OCHOBa 6iJILma BiA 6i'IHOlCTOpoHH Ha 3M.

12.AoseAiTL, ~o y piBHOCTOpOHHLOro 'l'PHKYTHHKasci KYTH piBHi.

13.BiA sepmHHH C piBHo6eApeHoro TPHKYTHHKa ABC a OCHOBOIO

AB BiAKJiaAeHo piBHi BiApiaKH: CA1 - Ha CTopoHi CA i CB1 - Ha cTopoui CB. AoseAiTL pisHiCTL TpHKYTHHKiB: 1) CAB 1 i

CBA 1; 2) ABB, i BAA1.

14.Ha ocHoBi AB piBHo6eApeHoro TpHKYTHHKa ABC AaHo TO'IKH A1 i B1. BiAOMO, ~o AB1 = BA1. AoBeAiTL, ~o TPHKYTHHKH

AB,C i BA1C piBHi.

15.TpHKYTHHKH ACC, i BCC1 piBHi. lx sepmHHH A i B JiemaTL

no piaHi 6oKH siA npHMo'i CC,.	AoBeAiTh, ~o TPHKYTHHKH
ABC i ABC, piBH06eApeHi (MaJI.	62).

16.C«l>opMyJlIOHTe i AOBeAiTL TeOpeMy, o6epHeHY AO TBepAmeHH$1 aaAa'li12.

17.Ha cTopouax AC i BC TpHKYTHHKa ABC BaHTo TO'IKHC 1 i C2. AoeeAiTL, ~o TPHKYTHHK ABC pi:eH06eApeHHH, HK~o TPHKYTHHKH ABC1 i BAC2 piBHi (MaJI. 63).

18.1) AoeeAiTL, ~o cepeAHHH cropiH pi:eHo6eApeuoro TPHKYTHHKa e TaKom BepmHHaMH piBHOOeApeHoro TPHKYTHHKa.

2)AoeeAiTh, ~o cepeAHHH cropiH piBHocTOpoHHLoro TPHKYTHHKa e TaKom BepmHHaMH piBHOCTOpOHHLOrO TPHKYTHHKa.

19.1) HaKpecJiiTL TPHKYTHHK a rOCTPHMH KYTaMH. 3a AODOMOrOIO KOCHH~$1 i JiiHiHKH npoeeAiTh y HLOMY BHCOTH. BHKOHaii:Te BnpaBy noBTOpHo AJIH TPHKYTHHKa, y HKoro OAHH KYT Tynuii:.

64).

1 KJiac	46
[	E

A

Man. 63

MaJI. 64

2)HaKpec.ni.Ti. TPHKYTHHK. 3a AOnoMoroio TpaucnoPTupa i .rri- uiiiKH npose,u;iTI> y HbOMY 6iceKTPHCH.

3)H&Kpec.ni.Ti. TPHKYTHHK. 3a AOnoMoroio niHiiiKH a noAiJIKaMH npose,u;iTb y HbOMY Mep;iaHH.

20• .D;oseAiTi., ~o y piBHo6eApeHoMy TPHKYTHHKy: 1) 6iceKTpHCH, nposeAeHi a sepmRH npH ocuosi, piBHi; 2) Me,u;iauu, nposeAeHi 3 THX caMHX eepmHH, TaKOXC piBHi.

21. .D;oseAiTi., ~o y piBHHx TpHKYTHHKaX ABC i A 1B1C1: 1) MeAia-

HH, nposeAeHi a sepIQHH A i Ai, piBui; 2) 6iceKTpucu, npoBeAeui a sepmHH A i Ai, pisui.

22. To11KH A, B, C, D nexcan ua OAHiii npBMiit, npH'IOMYsip;piaKH

AB i CD MaIOTh cniJii.uy cepeAHHY• .D;oseAiTh, ~o KOJIH TPHKYTHHK ABE piBHo6eApeHHii a ocuosoio AB, TO TpHKYTHHK CDE a ocuosoio CD TaKoxc pisuo6e.u;peud (Man.

23. .D;ose.u;iTb piBHiCTh TPHKYTHHKiB aa KYTOM, 6iceKTPHCOIO ~oro Kyra i CTOpOHOIO, npunerJIOIO AO HbOI'O.

24. Y piBHo6eApeHOMY TPHKYTHHKY ABC a ocuoeoio AC npoBeAeHo MeAiauy BM. Ha uiii yawro TO'IKYD. .D;oseAiTL pieHicTi. TpHKYTHHKis: 1) ABD i CBD; 2) AMD i CMD.

25. .D;oeeAiTi., ~o TPHKYTHHK ABC piBHo6eApeHHii, SK~o y ui.oro:

1)	Me,u;iaua BD e BHCOTOIO; 2) BHCOTa BD e 6iceKTpuco10;
3)	6iceKTpuca BD e Mep;iauoio.

26. .D;auo ABa piBHo6eApeHHX TPHKYTHHKH ia CniJibHOIO OCHOBOIO.

.D;oseAiTi., ~o ix MeAiaHH, npoBeAeHi AO ocHOBH, JiemaTi. ua OAuiii npaMiii.

27. Y piBHo6eApeHOMY TPHKYTHHKY ABC a ocuoeo10 AC nposeAeHo MeAiauy BD. 3uaiiAiTb IT AOBmuuy, aK~o nepuMeTP TPHKYTHHKa ABC AOpisuioe 50 M, a TPHKYTHHKa ABD - 40 M.

§ 3. 03H8J( H piBHOCTi TpHICyrHHKiB

47

[

A D

A

Man. 65

Man. 66

28.,lJ;oBeAin, JI\O 6iceKTpHca piBHo6eApeHoro TPHKYTHHKa, npoBeAeHa 3 sepmHHH, npoTHJie:>KHOi OCHOBi, G MeAiaHOIO i BHCOTOIO.

29.Y TPHKYTHHKax ABC i A1B1C1: AB= A1B1, AC= A1C1, LC= L Ci= 90°. ,lJ;oBeAiTi., JI\O /:::.ABC= /:::. A1B1C1.

30.,lJ;oBeA.iTb, II\O y piBHo6eApeHOMY TPHKYTHHKY BHCOTa, OBYJI\eHa Ha OCHOBY, e MeAiaHOIO i 6iceKTPHCOIO.

31.TpuKyTHHKH ABC i ABC1 i3 cnini.HoIO OCHOBOIO AB piBH0-

6eApeHi. ,lJ;oeeAiTi. piBHicTi. TpHKYTHHKiB ACC1 i BCC1.

32~ To'IKHA, B, C, D JiemaTi. Ha OAHiii npaMiii. ,lJ;oBeAiTi., JI\O KOJIH TpHKYTHHKH ABE1 i ABE2 piBHi, TO TPHKYTHHKH CDE1 i CDE2 TaKO:>K piBHi (MaJI. 65).

33.,D;ea BiApi3KH AB i CD nepeTHHaIOTbcR y TO'l~ 0, &Ka e cepeAHHOIO KO:>KHoro 3 HHX. ,lJ;oBeAiTb piBHicTi. TPHKYTHHKiB ACD i

BDC.

34.,lJ;oBeAiTb piBHiCTb TPHKYTHHKiB 3a ABOMa CTOpoHaMH i MeAiaHOIO, npoBeAeHOIO AO OAffiG'i3 HHX.

35.BiApi3Ku AB i CD nepeTHHa10nca. ,lJ;oBeAiTi., II\O KOJIH BiApi3KH AC, CB, BD i AD piBHi, TO npoMiHi. AB e 6iceKTpHco10 KyTa

CAD i npoMiHi. CD - 6iceKTpHco10 KyTa ACB (MaJI. 66).

36~ ,D;oseAiTi., JI\O B 3&Aa11i 35 npm.d AB i CD nepneftAHKYJI.RpHi. 37. TpHKyTHHKH ABC i BAD piBHi, npH'lOMYTO'IKHCi D JiemaTb no pi3Hi 6oKu BiA npaMo'iAB (MaJI. 67). ,lJ;oBeAiTi., II\O: 1) TPHKYTHHKH CBD i DAC piBHi; 2) npaMa CD AiJIHTb BiApiaoK

AB nonoJiaM.

38. BiApi3KH AB i CD OAHaKoBO'iAOBmHHH nepeTHHaIOTbCR B TO'I- ~ 0 TaK, JI\O AO= OD. ,lJ;oBeAiTi. piBHicTb TPHKYTHHKiB ABC i DCB.

7 KJiac	48
	[

Mil.II. 67

Man. 68

39.,IJ;oBeAiTb piBHiCTb TPHKYTHHKiB 38 ABOM8 CTOpoH8MH i MeAi8HOI<>, ~o BHXOA11Tb 3 O,ll;Hie'iBepmHHH (Ma.n. 68).

40.,IJ;oBeAiTb piBHiCTb TPHKYTHHKiB 38 CTOpOHOI<>, MeJU8HOIO, npoBeAeHOI<> AO He'i,i KYT8MH, 11Ki YTBOPI<>e MeAi8H8 i3 CTOpoHOI<>.

§4. CYMA KYTIB TPHKYTBllKA

29. IlAPAJIEJILIDCTb IlP.HMHX

Teo p e M 8 4.1. /.fsi npllMi, na.pauJ1.1>Hi rperi4, napa.J&ea'l>Hi ooHa o8Hiu.

,n; o Be A e H H 11. Hexaii npaMi a i b n8p8Jiem.Hi npaMiit c. IlpHnycTHMO, ~o np11Mi a i b He n8p8JieJibHi (M8JI. 69). ToAi BOHH nepeTHYTbCS B ,u;eBKiii To~i C. OTme, 11epe3 TO'IKYC npoxo,u;&Tb ABi npsMi, n8paJieJI1>Hi npaMiit c. AJie ~e HeMomJIHBO, 6o qepe3 roqKy,

~o He Jie)KHTb Ha ,ii;aHiii npaMiii, MO)KHa npoBecTH He 6iJibm SK OAHY npaMy, napaJieJibHY A8Hiii. TeopeMy ,u;oBe,u;eHo.

	3 a A a 11 a	( 4). Ilp11Mi AB i	CD napaJieJII>Hi. ,IJ;oBeAiTI>, ~o
	KOJIH si,ll;piooK BC nepeTHHae npsMy AD, TO ToqKa nepeTHHY
	H8Jl0)KHTb Bi,ll;pi3Ky AD (M&.11.		70).
:		a	x
	[	I

I

c

Man. 69

Man. 70

§ 4. CyMa KyTiB TPHICYTHHKa	49
Po a B'SI a a H H H. Hexaii X -	TO''IKanepeTJrny Bi,z:i;piaKa

BC a npSIMOIO AD. IIpoBe,z:i;eMo 11epea Hei'.npnMy x, napaJieJibHY npSIMiii AB. BoHa 6y,z:i;e napaJieJibHa i npSIMiii CD. IIpSIMa x poa6HBae nJio~HY Ha ,z:i;Bi niBnJIOID;HHH. To'IKHBi C JiemaTb y piaHHX niBnJIOID;HHax, 60 Bi,z:i;piaoK BC nepeTHHae npSIMy x (B TO'IWX). To11Ka A JiemHTb y Tiii caMiii niBnJIOID;HHi, m;o i B,

a TO'IKaD - y TiH	caMili niBilJIO~Hi, m;o i c. ToMy	Bi,z:i;pi-
30K AD nepeTHHae	npSIMY x. A TO'IKOIOnepeTHHY e	TO'IKa

XBi,z:i;piaKa BC.

30. KYTH, YTBOPEHI B PE3YJibTATI IIEPETHHY

,ll.BOX IIPHMHX CI1IHOIO

Hexaii AB i CD - ,z:i;Bi npSIMi i AC - TpeTSI npnMa, m;o nepeTHHae npnMi AB i CD (MaJI. 71). IIpSIMa AC Bi,z:i;HOCHO npHMHX AB i CD HaaHBa6TbCH ci'lno10.

IIapH KyTiB, SIKi yTBOJ>IOIOTbCH B peayJibTaTi nepeTHHY npHMHX AB i CD ci1JHOIO AC, MaIOTb cnewaJibHi Ha3BH.

Hl<m;o TO'IKHBi D JiemaTb B o,z:i;Hiii niBnJIOID;HHi BiAHOCHO npaMoi'.

AC, TO KYTH BAC i DCA Ha3HBaIOTbCJI 8HyrpiwniMU oanocroponniMu (Man. 71, a).

Hl<m;o TO'IKHB i D nemaTb y piaHHX niBnno~Hax BiAHOCHO npnMoi'.AC, TO KYTH BAC i DCA HaaHBaIOTbCH BHyrpiwniMu pi3nocroponniMu (Man. 71, 6).

Ci11Ha AC yTBop10e a npaMHMH AB i CD ,z:i;Bi napH BHyTpimHix OAHOCTOJ>OHHix i ,z:i;si napH BHyrpimHix piaHOCTOJ>OHHix KyTiB. BHyT-

8

a)

MaJI. 71