Uphawu lokuqala ukulingana zoonxantathu. Imiqondiso yesibini neyesithathu ukulingana zoonxantathu

Phakathi inani elikhulu weepholigoni, eyinxalenye non-ezidibanayo ivaliwe umgca polygonal, unxantathu - oyintsobi kunye nenani mncinane engile. Ngamanye amazwi, le buyimilo elula. Kodwa ke, nangona elula yayo, eli nani uyayigubungela ezininzi iimfihlelo kunye ezifunyaniswe umdla, nto leyo igqamisa isebe ezizodwa kwimathematika - geometry. Olu qeqesho ezikolweni baqalise ukufundisa kwibakala lesixhenxe, yaye "Triangle" umxholo inikwe ingqalelo ekhethekileyo. Abantwana ungafundi kuphela imithetho mzobo ngokwayo, kodwa ukuthelekisa yabo yokufunda-1, 2 no-3, uphawu ukulingana zoonxantathu.

I omaziyo lokuqala

Omnye imithetho yokuqala, baqhelene abafundi, iya into efana nale: umdibaniso engile kanxantathu ilingana degrees 180. Ukuqinisekisa oku, lwanele ukusebenzisa neprotrektha ukulinganisa ngalinye eziphezulu badibanise zonke amaxabiso ngenxa. Ngako oko, xa amaxabiso ezimbini eyaziwa ngokulula ukugqiba owesithathu. Umzekelo: Kwenye ikona lo nxantathu 70 °, yaye omnye - 85 °, yintoni ubungakanani engile wesithathu?

180 - 85 - 70 = 25.

Impendulo: ukuba ° 25.

Imisebenzi inokuba unzima ngakumbi, ukuba omnye kuphela engile ixabiso elimisiweyo ixabiso yesibini malunga wathi kuphela kangakanani okanye zingaphi izihlandlo luyayidlula okanye ngaphantsi.

Kulo nxantathu ukuba omnye okanye elinye iimpawu zayo ezikhethekileyo umgca, iyileyo yenziwe kuyo igama yayo:

• ukuphakama - umgca nkqo athathwe enekona kwelinye icala;
• zonke zontathu phezulu, kuqhutywa ngaxeshanye, embindini mzobo phambana, ukwakha orthocenter, leyo, ngokuxhomekeke kuhlobo lo nxantathu kunokuba zombini ngaphakathi nangaphandle;
• Amanqaku angumndilili - kumgca osuka phezulu ukuya embindini icala;
• esiyifundayo ekudibaneni kwe-medians sandla wayo, okungaphakathi imilo;
• bisector - line isebenza ukusuka phezulu ukuya kwindawo yonqumlo kunye icala, ingongoma ekudibaneni kwe-bisectors kathathu embindini wesangqa sibhalwe.

iinyaniso Simple malunga oonxantathu

Oonxantathu, njengokuba, eneneni, kwaye onke amanani abe neempawu zabo kunye neepropati. Njengoko sele kukhankanyiwe, lo mzobo yepholigoni elula, kodwa iimpawu zayo iimpawu:

• ngokuchasene engile kakhulu elide-icala kusoloko esukuba iyilala wukulu enkulu, yaye vice versa;
• nxazonke alinganayo-engile bayalingana, umzekelo - unxantathu isosceles;
• sum of the engile wezasekhaya isoloko ilingana 180 °, ukuba sele wabonisa umzekelo;
• uqhebeke kwelinye icala kanxantathu luqokelelane ngaphaya engile engaphandle eya kusoloko kulingana kwisixa se engile, iye ongagudlanga;
• nayiphi na amaqela usoloko ngaphantsi kwe isixa lwezinye macala mabini, kodwa ke inkoliso iyantlukwano yabo.

types of triangles

Ukukhangela kwisigaba esilandelayo kukuchonga iqela apho unxantathu thaca. Ilungu uhlobo oluthile kuxhomekeke amaxabiso-engile kanxantathu.

• Ayisoselisi - namaqela amabini alinganayo ngubani ekuthiwa icala, nowesithathu kule meko isebenza iimilo base. Le angles emazantsi nxantathu ezifanayo kunye udibaniso athathwe phezulu, le bisector nokuphakama.
• Lungisa, okanye unxantathu alinganayo - yenye apho yonke emacaleni aso bayalingana.
• Okoxande enye iikona zayo ° 90. Kulo mzekelo, icala le-engile ubizwa ngokuba hypotenuse, kunye nezinye ezimbini - imilenze.
• unxantathu Acute - zonke engile ngaphantsi ° 90.
• Obtuse - enye engile mkhulu kunaye ° 90.

Ukulingana kunye ukufana zoonxantathu

Xa inkqubo yokufunda akuxhomekekanga kuphela ngokwahlukileyo zicingeleka zimilile, kodwa kwakhona ukuba bathelekise oonxantathu ezimbini. Yaye lo mxholo obonakala esilula kakhulu imithetho kunye theorems leyo obubonisa ukuba inani ingqalelo - oonxantathu ngokulinganayo. Miqondiso oonxantathu kufuneka inkcazelo yokulingana: i oonxantathu ayalingana ukuba macala ehambelana kunye engile bayalingana. Ngesi lenxaki, ukuba iwise la manani bobabini, yonke imigca zabo livuma. Kwakhona nani inokuba efanayo, ingakumbi, kumayelana kakhulu iimilo ezifanayo, ezahlukeneyo kuphela ubukhulu. Ukuze wenze kwisigqibo enjalo phezu oonxantathu amelwe kufuneka yaneliswe omnye wale miqathango ilandelayo:

• angles ezimbini mzobo omnye ulingana engile ezimbini omnye;
• ngokomlinganiselo emacaleni omabini la macala omabini unxantathu yesibini, kwaye engile wamacala kwakhiwa bayalingana;
• amacala ezintathu yesibini mzobo iyafana naleyo yokuqala.

Kakade ke, ngenxa ukulingana ekuzibonakaliseni, oko akuthethi ukuba yokuthandabuza, kufuneka ube amaxabiso efanayo zonke izinto zombini manani, kodwa ke ingxaki le thiyori lula kakhulu, yaye kuphela iimeko ezimbalwa kuvunyelwa ukuba babe nobungqina ukuba oonxantathu.

Uphawu lokuqala ukulingana zoonxantathu

kwi sihloko iingxaki zisonjululwe ngokusekelwe ubungqina theorem, leyo ifundeka ngolu hlobo lulandelayo: ". Ukuba macala omabini lo nxantathu kunye engile leyo zakha, ayalingana macala omabini kunye engile omnye unxantathu, ngoko amanani kwakhona lingana omnye komnye"

Njengokuba ubungqina isandi theorem malunga lowokuqala umqondiso yokulingana zoonxantathu? Wonke umntu uyazi ukuba inxalenye emibini iyalingana ukuba babe ubude enye, okanye umtya ojikeleyo ngokulinganayo ukuba babe radius efanayo. Kwaye kwimeko nxantathu kukho iimpawu ezimbalwa apho kunokuthi ke kuthathwe ukuba amanani ziyafana, leyo luncedo kakhulu ekucombululeni iingxaki ezahlukeneyo yemigca.

Isandi theorem "Uphawu lokuqala ukulingana zoonxantathu", ezichazwe ngasentla, kodwa ubungqina yayo:

• unxantathu Masithi ABC ne A ₁ B ₁ C ₁ emacaleni efanayo AB kunye A ₁ B _1, ngokulandelelana, BC no B ₁ C _1, kwaye engile ukuba akhiwa ezi emacaleni anexabiso efanayo, ngamanye ngokulinganayo. Emva koko wasibeka phezu ABC △ △ A ₁ B ₁ C _1, sifumana umdlalo yonke imigca kunye eziphezulu. Oku kulandela ukuba ezi oonxantathu ncam, ethetha ngokulinganayo.

Theorem "Uphawu lokuqala ukulingana zoonxantathu," ekwabizwa ngokuba "macala omabini kunye ikona." Enyanisweni, oku eyona nto.

Theorem kwi sesibili

Uphawu yesibini wokulingana kwaba ngokufanayo, ubungqina isekelwe kwinto yokuba nokubekwa iziqwenga kwi enye kwenye, ukuba twatse ezincotsheni zonke namacala. A theorem izandi ngolu hlobo: "Ukuba kwicala elinye kunye angles ezimbini ekubunjweni apho inxaxheba, i-Party kunye ezimbombeni zaso ezimbini unxantathu yesibini, ngoko la manani ziyafana, okt ngokulinganayo."

Uphawu lesithathu kunye nobungqina

Ukuba bobabini 2 kunye umqondiso 1 ukulingana isebenza kuzo zombini amacala oonxantathu, ububanzi iimilo, eyesithathu ibhekisela kuphela kumaqela. Ngoko ke, lo theorem unalo amagama ulandelayo: "Ukuba onke macala unxantathu ayalingana emacaleni ezintathu unxantathu yesibini, le mifanekiso ncam."

Ukungqina oku theorem, kuyimfuneko ukuba lokuhlolisisa ngokweenkcukacha omkhulu kwinkcazelo ukulingana. Enyanisweni, oko kuthethwa "oonxantathu bayalingana"? Identity ithi ukuba inyanzelise inani omnye komnye, zonke izinto ezifana, kusenokuba njalo xa emacaleni zabo engile bayalingana kuphela. Ngelo xesha linye i-engile malunga icala elinye, yona iyafana omnye unxantathu lilingana enekona ohambelana sesibini mzobo. Kufuneka kuqatshelwe ukuba ngelo xesha ubungqina kulula ukuba ukuguqulela lwezandla 1 ukulingana zoonxantathu. Ukuba olu landelelwano ithe waphawula, ukulingana triangles nje akunakwenzeka, ngaphandle kwakwiimeko apho mzobo umfanekiso isipili lokuqala.

oonxantathu Right

Ubume zoonxantathu ezinjalo kusoloko enekona kunye engile 90 °. Ngoko ke, le nkcazelo zilandelayo ziyinyaniso:

• oonxantathu nge esinekona sasekunene ayalingana ukuba imilenze cathetus yesibini ncam;
• amanani ayalingana ukuba bayalingana ukuya hypotenuse omnye imilenze;
• oonxantathu ezinjalo ayalingana ukuba imilenze yabo engile efana bukhali.

Olu phawu inxulumene oonxantathu buxande. Ukungqina theorem kusetyenziswa iimilo app omnye komnye, oko kukhokelele imilenze oonxantathu isongiwe ukuze ezimbini ngqo ekhohlo engile ngqo _ne-CA-1 kunye namacala CA.

bangazisebenzisa

Kwiimeko ezininzi, xa kusenziwa oku, isicelo uphawu lokuqala ukulingana zoonxantathu. Enyanisweni, lo iklasi ebonakala ilula ukuze geometry moya nejiyometri umxholo ezisetyenzisiweyo 7 ukubala ubude, umzekelo, intambo ifowuni ngaphandle kwindawo womlinganiselo, apho kuya kwenzeka. Ukusebenzisa le theorem kulula ukwenza izibalo kuyimfuneko ukuze kube nokugqitywa ubude siqithi, ibekwe phakathi komlambo, ngaphandle kuqubha kuyo. Okanye baqinise ucingo ngokubeka bar kwi ibheyi ukwenzela ukuba yahlulwe oonxantathu amabini alinganayo, okanye ukubala izinto ezintsonkothileyo zomsebenzi bokuchwela okanye ekubaleni lwenkqubo truss lophahla ngexesha lokwakha.

Uphawu lokuqala ukulingana zoonxantathu usetyenziswe ngokubanzi kwi "abadala" ubomi benene. Ngoxa kwiminyaka aphezulu esikolweni kuba sesona sihloko abaninzi kubonakala uyadika kunye engeyomfuneko ngokupheleleyo.