Unxantathu obumnyama: ubude bezinhlangothi, inani lama-angles. Unxantathu othosiwe uchazwe

Noma kunjalo izingane zasenkulisa ziyazi ukuthi unxantathu ubukeka kanjani. Kodwa yilokho abayikho, la madoda asevele eqala ukuqonda isikole. Uhlobo olulodwa unxantathu obuthile. Qonda ukuthi iyini, indlela elula, uma ubona isithombe ngesithombe sayo. Futhi ngombono lokhu kubizwa ngokuthi "i-polygon elula" enezinhlangothi ezintathu nama-vertices, okunye okuyi- angle e-obtuse.

Qonda imibono

E-geometry, lezi zinhlobo zezibalo ezinezinhlangothi ezintathu zihlukaniswa: izintathu ezinamaqenqema, ezinamacala angama-rectangular and obtuse. Izakhiwo zalezi polygon ezilula zifanayo kubo bonke. Ngakho-ke, kuzo zonke izinhlobo ezibalulwe ukungalingani okunjalo kuzobanjwa. Isibalo sobude bezinhlangothi ezimbili sizoba mkhulu kunebude besithathu.

Kodwa ukuze uqiniseke ukuthi uyisiqalo esiphelile, hhayi isethi yama-vertices ngamunye, kuyadingeka ukuqinisekisa ukuthi isimo sesisekelo sihlangene: inani lama-angles obunxantathu obtuse lingu-180 ^° . Okufanayo nakwezinye izinhlobo zezinombolo ezinezinhlangothi ezintathu. Kuyiqiniso, kunxantathu ene-obtuse, enye yama-angles iyoba ngaphezu kwe-90 ^° , kanti lezi ezimbili ezisele zizobukhali. Kulolu cala, i-angle enkulu kunazo zonke izobe ibhekene nohlangothi olude kakhulu. Iqiniso, lokhu akuzona zonke izakhiwo zezinxantathu ezine-obtuse. Kodwa ukwazi lezi zici kuphela, abafundi bangaxazulula izinkinga eziningi geometry.

Kuzo zonke i-polygon ezinama-vertices amathathu, kuyiqiniso futhi ukuthi, uma siqhubeka ngapha nangapha, sithola i-angeli obuso bayo obulingana nesamba sezingqimba ezimbili zangaphakathi ezingekho eduze. Umjikelezo wendwangu yesibhakabhaka ibalwa ngendlela efanayo nezinye izibalo. Ilingana nesibalo sobude bazo zonke izinhlangothi zalo. Ukuze unqume indawo yongxantathu, izazi zezibalo zathola amafomu ahlukahlukene, kuye ngokuthi iyiphi idatha ekhona ekuqaleni.

Umklamo oqondile

Esinye sezimo ezibaluleke kakhulu ekuxazululeni izinkinga ku-geometry yisilinganiso esifanele. Ngokuvamile othisha bezibalo bathi ngeke kusize ngeso lengqondo lokho okunikezwayo nokuthi yini edingekayo kuwe, kodwa u-80% usondelene nempendulo efanele. Yingakho kubalulekile ukwazi ukwakha unxantathu obumnyama. Uma nje udinga isibalo sokucabanga, khona-ke ungakwazi ukudweba noma yiliphi i-polygon ngezinhlangothi ezintathu ukuze elinye lamabhande likhulu kunama- ^degree angu-90.

Uma izinhlangothi ezithile noma ama-degree of angles anikezwa, ke ukudweba kathathu kunesidingo ngokuhambisana nabo. Ngokwenza kanjalo, kubalulekile ukuzama ukuchaza ngokunembile ama-angles, ukubala ngabo ngosizo lwe-protractor, futhi ngokulinganayo nedatha ezimweni zomsebenzi ukubonisa izinhlangothi.

Imigqa eyisisekelo

Ngokuvamile, abafundi abanalo okuningi ukwazi ukuthi lezi noma ezinye izibalo kufanele zibuke kanjani. Awukwazi ukukhawulelwa kuphela ngolwazi mayelana nokuthi iyiphi unxantathu obhekile futhi okuyi-rectangular. Isifundo semathematika sichaza ukuthi ulwazi lwabo ngezici eziyinhloko zamanani kufanele luphelele.

Ngakho-ke, umfundi ngamunye kufanele aqonde incazelo ye-bisector, ephakathi, ephakathi nendawo yokuphakama nokuphakama. Ngaphezu kwalokho, kumele azi kanye nezakhiwo zabo eziyinhloko.

Ngakho-ke, ama-bisectrix ahlukanisa i-engeli ngesigamu, futhi uhlangothi oluphambene - zibe izingxenye ezilingana nezinhlangothi eziseduze.

Umphakathi uhlukanisa noma iyiphi inxantathu ibe yizindawo ezimbili ezilinganayo. Ngalinye iphuzu lapho lihlangana khona, ngamunye wabo uhlukaniswe ngezigaba ezimbili ngo-2: 1 isilinganiso, uma ubhekwa kusuka phezulu avela kuwo. Kulesi simo, i-median enkulu ivame ukudonsa eceleni.

Ukunakwa okuncane kunakhokhelwa ekuphakameni. I-perpendicular kuya ehlangothini oluphambene ukusuka ekhoneni. Ukuphakama kwendunxantathu e-obtuse kunezici zayo. Uma idonselwa kusuka ku-vertex enzima, ke ayiwi ohlangothini lwale polygon elula, kodwa ngokuqhubeka kwayo.

I-central perpendicular iyisigaba esivela esiphakathi kobuso besonxantathu. Ngesikhathi esifanayo, itholakala kuma-angles angakwesokudla.

Ukusebenza imibuthano

Ekuqaleni kokutadisha i-geometry, kwanele ukuba izingane ziqonde ukuthi zidweba kanjani unxantathu obumnyama, ukuze ufunde ukuthi ungayahlukanisa kanjani nezinye izinhlobo zezilwane futhi ukhumbule izakhiwo zayo eziyisisekelo. Kodwa abafundi abaphezulu balolu lwazi kakade bancane. Isibonelo, ku-EGE kaningi kunemibuzo ngokulandelana nokubhalwa. Eyokuqala yalezi zinkinga zonke izintathu ezintathu zontathu, kanti okwesibini kunephuzu elilodwa elivamile nazo zonke izinhlangothi.

Ukwakha unxantathu obhalwe phansi noma ochazwe ngokucacile kakade kunzima kakhulu, ngoba lokhu kuyadingeka kuqala ukuthola ukuthi isiphi isiyingi sombuthano kanye nengqikithi yayo kufanele ibe. Ngendlela, kuleli cala hhayi kuphela ipensela enombusi, kodwa futhi ikhampasi iba ithuluzi elidingekile.

Izinkinga ezifanayo ziphakama lapho kwakhiwa ama-polygons abhalwe ngezinhlangothi ezintathu. Ababalo bezesayensi baye bathola amafomu ahlukahlukene okwenza kube lula ukunquma indawo yabo ngokunembile ngangokunokwenzeka.

Izintathu ezibhalisiwe

Njengoba kushiwo ngaphambili, uma umbuthano udlula kuwo wonke ama-vertices amathathu, lokhu kubizwa ngokuthi umbuthano ojikelezayo. Impahla yayo eyinhloko ukuthi yiyodwa kuphela. Ukuze uthole ukuthi umjikelezo ojikelezayo wesigcawu esiphezulu kufanele utholakale kanjani, kufanele ukhunjulwe ukuthi isikhungo saso sisemkhatsini wezinhlangothi ezintathu eziphakathi ezihamba phambili eziya ezinhlangothini zalesi sibalo. Uma i-polygon ene-angled ene-angled enezingqimba ezintathu leli phuzu lizoba phakathi kwalo, khona-ke ku-polygon i-obtuse kuyoba ngaphakathi kwayo.

Ukwazi, isibonelo, ukuthi enye yamacala enxantathu e-obtuse ilingana nengqikithi yayo, umuntu angathola i-angle ehlangene nobuso owaziwayo. I-sine yayo izolingana nomphumela wokuhlukanisa ubude ohlangothini owaziwa ngu-2R (lapho iRadio engxenyeni yombuthano). Okungukuthi, i-angle yesono izolingana no-½. Lokhu kusho ukuthi i-angle iyisi-150 ^° .

Uma udinga ukuthola indawo engxenyeni ejikelezayo yesigcawu esiphezulu, uzodinga ulwazi mayelana nobude bezinhlangothi zalo (c, v, b) nendawo yalo S. Emva kwakho konke, irejista ibalwa kanje: (c x v x b): 4 x S. Ngendlela, , Uhlobo luni lomdwebo: unxantathu obtuse othomathikhi, ama-isosceles, eqondile noma acute. Kunoma yisiphi isimo, ngenxa yesimiso esingenhla, ungathola indawo ye-polygon enikeziwe ngezinhlangothi ezintathu.

Izintathu ezintathu ezichazwe

Futhi, ngokuvamile kufanele usebenze ngemibuthano ebhaliwe. Ngokomunye wamafomula, irejista yaleso sibalo, ephindwe ngamaphesenti angu-½, iyolingana nendawo yohantathu. Noma kunjalo, ngokucaciswa kwalo udinga ukwazi izinhlangothi zesigcawu esiphezulu. Emva kwakho konke, ukuze unqume u-½ umjikelezo, udinga ukwengeza ubude bawo bese uhlukanisa ngo-2.

Ukuze uqonde ukuthi kuphi isikhala sombuthano esibhalwe kunxantathu e-obtuse kufanele kube, ama-bisectors amathathu kufanele adonselwe. Lezi yimigqa ehlukanisa ama-angles ngesigamu. Kusemkhakheni wabo futhi kuzoba phakathi kwendilinga. Kulesi simo, kuyoba equidistant kusuka ohlangothini ngalunye.

Ingqikithi yombuthano onjalo olotshwe kunxantathu e-obtuse ilingana nomsuka wesikwele we-quotient (pc) x (pv) x (pb): p. Kulesi simo, i-p isilinganiso sokuqala sezinxantathu, c, v, b yizinhlangothi zawo.