Uphawu lokuqala nokulingana onxantathu. Izibonakaliso nokulingana onxantathu wesibili nowesithathu

Phakathi nesibalo esikhulu ngemapholigoni, okuyinto empeleni non-intersecting ivaliwe umugqa zikanhlangothiningi, unxantathu - kuyinto sibalo nenani okungenani ka-engeli. Ngamanye amazwi, kuba ipholigoni elula. Kodwa, naphezu alula, lesi sibalo uyazifihla eziningi izimfihlakalo ethakazelisayo, eqokomisa igatsha ekhethekile wezibalo - izibalo zama-engela. Lokhu isiyalo ezikoleni uqale efundisa ibanga lesikhombisa, futhi "Triangle" indaba ephathwayo kunikezwa ukunakekelwa okukhethekile. Izingane hhayi kuphela ukufunda imithetho sibalo ngokwayo, kodwa futhi ukuqhathanisa ukufunda 1, 2 no-3, kuwuphawu nokulingana onxantathu yabo.

Ukwazana lokuqala

Omunye wemithetho lokuqala, bajwayelene abafundi, iyaqhubeka okuthile okunjengokuthi: isamba engeli unxantathu kulingana 180 degrees. Ukuqinisekisa lokhu, lwanele ukusebenzisa protractor ukukala ngayinye vertices bese wengeza up wonke amagugu okuholela. Ngakho, lapho amanani amabili eyaziwa kalula ukunquma lwesithathu. Ngokwesibonelo: Kokunye ekhoneni unxantathu 70 °, kanti omunye uyisisebenzi - 85 °, lokho ubukhulu engela wesithathu?

180 - 85 - 70 = 25.

Impendulo: 25 °.

Imisebenzi kungaba more xaka, uma eyodwa kuphela eshiwo engela ukubaluleka kanye value yesibili mayelana wathi kuphela kangakanani noma kaningi kangakanani mkhulu noma ngaphansi.

Esikhathini unxantathu ukunquma elilodwa noma kwenye izici zayo ezikhethekile komugqa, ngalinye elikwazi kwenziwe ke unegama ayo:

• ukuphakama - emgqeni perpendicular sisuselwa vertex ukuba uhlangothi;
• zonke eziphakeme ezintathu, olwenziwa ngesikhathi esifanayo, maphakathi sibalo aphambana, ukwakha orthocenter, okuyinto, kuye ngohlobo unxantathu kungaba ngaphakathi nangaphandle;
• Median - umugqa ohlanganisa phezulu kuya maphakathi uhlangothi;
• iphuzu empambana we medians ka namandla aso, ongaphakathi ukuma;
• bisector - umugqa egijima kusukela phezulu kuze kube seqophelweni ezimpambanweni zomgwaqo uhlangothi, iphuzu empambana we bisectors amathathu maphakathi umbuthano olotshiwe.

amaqiniso Simple mayelana onxantathu

Triangles, njengoba ngempela futhi bonke izibalo anezici yabo nezimpahla. Njengoba sekushiwo, lesi sibalo a ipholigoni elula, kodwa izici zayo siqu isici:

• ngokumelene engela kakhulu eside-side njalo elala ezidlula abakhulu, futhi okuphambene nalokho;
• ngokumelene amacala alingane kukhona engeli alinganayo, isibonelo - unxantathu isosceles;
• isamba engeli Ingaphakathi uhlale elilingana 180 °, osekuvele wabonisa isibonelo;
• kwakhiwa kuyoshaya kwelinye uhlangothi unxantathu awunakuqhathaniswa-engeli yangaphandle okuzokwenza njalo ilingana nenani lezinombolo of engeli, it has hhayi eduze;
• yimiphi amaqembu uhlale esingaphansi isamba nezinye izinhlangothi ezimbili, kodwa iningi ukungezwani kwawo.

izinhlobo onxantathu

Ufuna esigabeni esilandelayo ukuhlonza iqembu lapho unxantathu ethulwa. Ukuba Ngowenkolo uhlobo oluthile kuncike amagugu engeli calantsatfu.

• Isosceles - namalungu amabili alinganayo owanibiza uhlangothi, eyesithathu kuleli cala uba base bobunjwa. I-engeli ngasesinqeni se unxantathu kuyafana futhi imidiyeni sisuselwa phezulu, iyona bisector futhi ukuphakama.
• Lungile, noma unxantathu equilateral - ingenye lapho zonke izinhlangothi zalo bayalingana.
• Kukanxande omunye emakhoneni salo 90 °. Kulokhu, uhlangothi lokhu engela ubizwa ngokuthi hypotenuse, kanti lawa amanye amabili - imilenze.
• unxantathu olunamandla - zonke engele engaphansi kuka-90 °.
• Obtuse - omunye engeli okukhulu kuka-90 °.

Amalungelo Alinganayo Nokuhlonipha ukufana onxantathu

Ngo inqubo yokufunda akugcini nje babhekwa eceleni zithathwe ukuma, kodwa futhi ukuqhathanisa aboncantathu ababili. Futhi lokhu obonakala ulula indaba ephathwayo has a lot of imithetho futhi theorems okungase kube nobufakazi bokuthi sibalo kubhekwa - onxantathu alinganayo. Izimpawu onxantathu abe kwencazelo ukulingana: aboncantathu ziyalingana uma izinhlangothi zabo ohambelana nama-engeli bayalingana. Nale equation, uma thina abeke lezi zibalo ezimbili kwa each nye, yonke imigqa yabo izingxenye. Futhi isibalo ingase isebenze ngendlela efana, ngokukhethekile, kumayelana kakhulu bobunjwa ezifanayo, ezingafani kuphela ezidlula. Ukuze wenze ukuphetha ngale ndlela ngokubheka onxantathu emelelwa okumelwe kubhekanwe nazo omunye kwale mibandela elandelayo:

• ezimbili engeli eyodwa sibalo ilingana ezimbili engeli yomunye umuntu;
• wakhona sezinhlangothini zombili ze-sezinhlangothini zombili ze-unxantathu yesibili, futhi engele izinhlangothi kwakhiwa bayalingana;
• izinhlangothi ezintathu sibalo yesibili kuyafana ukuthi wokuqala.

Yiqiniso, ukuze ukulingana ongenambangi, okuyinto akakubangeli ukuthi kuncane, kufanele ube nezindinganiso ezifanayo kuzo zonke izakhi kokubili izibalo, kodwa inkinga kwemfundiso yokuziphendukela lula kakhulu, futhi kuphela izimo ezimbalwa uvumelekile ukuba abe ukufakazela ukuthi onxantathu.

Uphawu lokuqala nokulingana onxantathu

ngesihloko izinkinga isixazululekile ngesisekelo ubufakazi theorem, esifundeka kanje: ". Uma-ke enhlangothini zombili unxantathu kanye engela okuyinto akha, ayalingana izinhlangothi ezimbili kanye engela omunye unxantathu ke izibalo nazo ulingana nomunye"

Njengoba ubufakazi umsindo theorem mayelana kuqubuka nokulingana onxantathu? Wonke umuntu uyazi ukuthi kumasegmenti ababili bayalingana uma banayo nobude obufanayo, noma selilonke alinganayo uma benamakhono engaba efanayo. Futhi endabeni unxantathu zikhona izimpawu ezimbalwa ngalo ke kungenziwa bazitshela ukuthi izibalo ayafana, okuwusizo kakhulu ekuxazululeni izinkinga ezihlukahlukene weJiyomethri.

Umsindo theorem "Uphawu lokuqala nokulingana onxantathu", ezichazwe ngenhla, kodwa ubufakazi bayo:

• Ake sithi unxantathu ABC kanye A ₁ B ₁ C ₁ kukhona izinhlangothi efanayo AB _no-1 B ₁ futhi, ngokulandelana, BC B ₁ C _1, kanye nama-engeli ukuthi akhiwa lezi zinhlangothi bangu efanayo, okungukuthi alinganayo. Khona-ke wasibeka phezu ABC △ △ A ₁ B ₁ C _1, sithola ukufana zabo bonke imigqa kanye vertices. Lokho kusho ukuthi lezi onxantathu ziyefana, okusho alinganayo.

Theorem "Uphawu lokuqala nokulingana onxantathu, 'obizwa nangokuthi' On izinhlangothi ezimbili futhi ekhoneni." Empeleni, lesi luwumgogodla ke.

Theorem uphawu lwesibili

Sesibili kokulingana kubonakaliswa efanayo, ubufakazi kusekelwe yokuthi ukunqunywa izingcezu ku each nye they ayafana kuwo wonke eziqongweni izinhlangothi. A theorem umsindo kanje: "Uma uhlangothi futhi engeli amabili kwetinhlavu lapho khona uhlanganyela, iQembu kanye ezimbili amakhona unxantathu yesibili, khona-ke lezi zibalo ayafana, okusho alinganayo."

Isibonakaliso yesithathu kanye nobufakazi

Uma kokubili 2 kanye 1 uphawu ukulingana kusebenza kuzo zombili izinhlangothi onxantathu, engeli nomumo, eyesithathu sibhekisela kuphela amaqembu. Ngakho, theorem inamazwi elandelayo: "Uma zonke izinhlangothi unxantathu ayalingana ezinhlangothini ezintathu unxantathu yesibili, izibalo ayafana yini."

Ukuze afakazele lokhu theorem, kubalulekile kokubuka ngokuningiliziwe ekuchazweni ukulingana. Eqinisweni, kwakusho ukuthini-ke "onxantathu bayalingana"? Identity uthi uma thina abeke omunye sibalo komunye, zonke izici ukufanisa, kungaba kuphela icala uma izinhlangothi yawo nama-engeli bayalingana. Ngesikhathi esifanayo i-engeli okuphambene ngalapha, okuyinto kuyafana nezinye unxantathu uyalingana vertex elihambisana sibalo yesibili. Kufanele kuqashelwe ukuthi kuleli qophelo ubufakazi kulula ukuhumusha ku 1 uphawu nokulingana onxantathu. Uma lokhu ukulandelana is hhayi waphawula, lo nokulingana onxantathu akunakwenzeka, ngaphandle ezimweni lapho bangamaphesenti nesibuko isithombe sokuqala.

onxantathu Kwesokudla

Isakhiwo onxantathu ezinjalo njalo vertex ngodobo 90 °. Ngakho-ke, izitatimende ezilandelayo ziyiqiniso:

• onxantathu ngodobo kwesokudla ziyalingana uma imilenze cathetus yesibili ezifanayo;
• izibalo ziyalingana uma ilingane hypotenuse futhi omunye imilenze;
• onxantathu enjalo ziyalingana uma kuphulwe imilenze yabo futhi ezifanayo engela oyingozi.

Lesi sici iphathelene onxantathu unxande. Ukuze afakazele Theorem esetshenziswa lokusebenza izimo nomunye, okuholela imilenze onxantathu ezigoqwe ukuze uqonde kwesokunxele ezimbili engela ngqo nge-CA ₁ nama-CA izinhlangothi.

ngokoqobo

Ezimweni eziningi, empeleni ke isicelo kuqubuka nokulingana onxantathu. Empeleni, lesi sigaba obonakala ulula ngoba geometry futhi indiza geometry esetshenziswa Ingcikitsi 7 ukubala ubude besikhathi, isibonelo, intambo yocingo ngaphandle ukulinganiswa kwendawo, lapho-ke kuzokwenzeka. Ukusebenzisa le theorem kulula ukwenza izibalo ezidingekayo ukunquma ubude isiqhingi, elise phakathi komfula, ngaphandle ebhukuda yonkana ke. Noma baqinise kocingo ngokubheja ibha olwandle ukuze lihlukaniswe onxantathu amabili alinganayo, noma ukubala izakhi ukuba inkimbinkimbi kwalowo msebenzi lokubaza noma kulesi sibalo truss ophahleni uhlelo ngesikhathi kwakhiwa.

Uphawu lokuqala nokulingana onxantathu has isicelo ebanzi endaweni yangempela "omdala" ukuphila. Nakuba eminyakeni esikoleni esiphakeme kuba isihloko kwabaningi ubonakala yisicefe futhi ngokuphelele engadingekile.