Unokufumana njani ukuphakama kwinqathathu engxowankulu? Ifom yokufumana, izakhiwo zokuphakama kwixantathu ye-isosceles

IJometri ayiyona into esikolweni, apho kufuneka ufumane uvavanyo oluhle. Kwakhona nolwazi olufunekayo ebomini. Ngokomzekelo, xa uwakha indlu ngophahla oluphezulu, kufuneka ubale ubukhulu beemithi kunye nenani labo. Oku kulula ukuba uyazi ukuba ungayifumana njani ukuphakama kwinqunxantathu ye-isosceles. Izakhiwo zokwakha zisekelwe ekufundeni iipropati zeejometri. Iifom zezakhiwo zihlala zibonakala zifana nabo. Iipramramid zaseYiputa, iipakethi kunye nobisi, ubuciko bezobuciko, iingqungquthela ezisenyakatho kunye neepatties zizo zonke izixantathu ezungeze umntu. Njengoko uPlato uthe, ihlabathi lonke lisekelwe kwiingxantathu.

Unxantathu we-isosceles

Ukwenza kucace, kuya kuxutyushwa ntoni ngokulandelayo, kuyafaneleka ukukhumbula izinto ezisiseko zeJometri.

Inxantathu i-isosceles ukuba inamacala amabini alinganayo. Bahlala bebizwa ngokuba yi-lateral. Icala, ubungakanani obuhlukeneyo, babibizwa ngokuba yizizathu.

Iingcamango ezisisiseko

Njengazo nayiphi na isayensi, i-geometry ineemigaqo yayo kunye neengcamango. Kukho ezininzi. Cinga kuphela abo ngaphandle kwesihloko sethu esiya kuqondakala.

Ukuphakama ngumgca ochanekileyo ogqithwe kwi-perpendicular kwelinye icala.

I-median yinkalo ejoliswe kuyo nayiphi na i-vertex yongxantathu kuphela ukuya phakathi kwecala.

I-bhisikidi ye-angle i-ray eyahlula i-angle kwihafu.

Umxube wexantathu umgca wecala, okanye kunoko, inxalenye yebhayisiki yekona, ukudibanisa i-vertex ngokubhekiselele.

Kubalulekile ukuba ukhumbule ukuba i-bhisikidi ye-angle iyimfuneko ye-ray, kwaye umsikisi wengxantathu uyinxalenye yolu hlobo.

Iibhontshisi kwisiseko

I-theorem ithi ii-angles ezisezantsi kwiphina inxantathu ye-isosceles zihlala zilingana. Kulula kakhulu ukubonakalisa le ngqungquthela. Cinga i-isosceles inxantathu ye-ABC iboniswe, apho i-AB = BC. Kusuka kwi-angle ye-ABC kuyimfuneko ukudweba i-bister ye-VD. Ngoku khawucinge ngamathantathu amabini afunyenweyo. Ngokwimeko ye-AB = BC, icala le-AP yee-triangles liqhelekileyo, kwaye ii-angles ze-AVD kunye ne-SVD zilingana, kuba i-VA ngumabhinki. Ukukhumbula isibonakaliso sokuqala sokulingana, sinokuphetha ngokugqibeleleyo ukuba ii-triangles ezicatshangelwayo zilingana. Kwaye ke, zonke ii-angles ezihambelana zilinganayo. Kwaye, ke, amaqela, kodwa ngeli nqaku siya kubuya kamva.

Ukuphakama kwexantathu ye-isosceles

I-theorem eyintloko apho isisombululo malunga nayo yonke ingxaki isekelwe ngolu hlobo: ukuphakama kwinqatyana ye-isosceles yintsimbi kunye ne-median. Ukuqonda intsingiselo yayo (okanye isitshixo), kubalulekile ukwenza isibonelelo esincedisayo. Ngenxa yoko kuyimfuneko ukusika unxantathu we-isosceles kwiphepha. Indlela elula yokwenza oku ivela kwi-sheet standard yeTetrad kwiseli.

Gcwalisa unxantathu obangela ukuba ube ngumyinge, ulungelelanise amacala. Kwenzekani? Amabini amathathu alinganayo. Ngoku kufuneka uhlolisise ukuqikelela. Ukuvelisa i-origami. Dweba umgca wefayile. Ukusebenzisa i-protractor, jonga i-angle phakathi komgca odweliwe kunye nesiseko senxantathu. Yithini i-angle ye-90 degrees? Inyaniso yokuba umgca odwetshiwe ngowona. Ngcaciso - ubude. Indlela yokufumana ukuphakama kwixantathu ye-isosceles, siyilungisa. Ngoku makhe sihlangabezane neembombo eziphezulu. Ukusebenzisa umqhubi ofanayo, jonga iilwimi ezibunjwe ngoku ngokuphakama. Ba lingana. Ngenxa yoko, ukuphakama kwakhona kumabhinki. Ukuxhotywe ngumlawuli, linganisa ubude apho ubude besiseko buqhekeka khona. Ba lingana. Ngenxa yoko, ukuphakama kwincantathu ye-isosceles ukwahlula isiseko kunye nesisombululo.

Ubu bungqina bolu bume

Uboniso olubonakalayo lubonisa ngokucacileyo inyaniso ye-theorem. Kodwa iJometri - inzululwazi ichanekile, ngoko ifuna ubungqina.

Ngethuba lokuqwalasela ukulingana kweenglesisi kwisiseko, ukulingana kwama-triangles kwaboniswa. Khumbula i-VD ngumbhayisiki, kwaye iinqununu ze-AED ne-SVD zilingana. Isiphetho sasi: le macala ahambelana nomxantathu kwaye, ngokuqinisekileyo, ii-angles zilingana. Ngenxa yoko, AD = SD. Ngoko ke, i-VD ingumlambo. Kuhlala ukubonisa ukuba iVD ubude. Ukuqhubela phambili ngokulingana kwama-triangles phantsi kokucatshungulwa, kuvela ukuba i-angle ye-ADB ilingana nekota ye-VDV. Kodwa ezi ngxumbini zombini zidibene, kwaye, njengoko ziyaziwayo, zinika i-180 degrees. Ngoko ke, bafanani na? Kakade, i-90 degrees. Ngaloo ndlela, i-VD kukuphakama kwixantathu ye-isosceles ifakwe kwisiseko. Njengoko kufunwa ukubonisa.

Iinkalo eziphambili

• Ukuze uphendule ngempumelelo iingxaki, umntu kufuneka akhumbule iimpawu ezisisiseko ze-isosceles triangles. Kubonakala ngathi zichasene nemibandela.
• Ukuba kwimeko yokuxazulula ingxaki ukulingana kweengalo ezimbini kufunyenwe, ngoko ujongene nomxantathu we-isosceles.
• Ukuba kwakunokwenzeka ukubonakalisa ukuba umlambo uxeshanye ubude bendxantathu, ngokugqibeleleyo ugqiba ukuba unxantathu iisosceles.
• Ukuba i-bhisikidi inokuphakama, ngoko, ngokusekelwe kwimpawu eziphambili, unxantathu ubizwa ngokuba yi-isosceles.
• Kwaye, ke, ukuba umlambo uvela kwindima yokuphakama, ngoko unxantathu u-isosceles.

Ukuphakamisa umhlathi 1

Nangona kunjalo, ngenxa yeengxaki ezininzi kufuneka ukuba ufumane ubude be-arithmetic. Yingakho sicinga indlela yokufumana ukuphakama kwixantathu ye-isosceles.

Masibuyele kumfanekiso ongezantsi apha, u-ABC, apho i-side, in-base. I-VD ubude bolu nxantathu, unokwakheka h.

Yintoni unxantathu we-AED? Ekubeni i-VD kukuphakama, inxantathu ye-AVD iyinxantathu, i-cathet yayo iya kufumaneka. Ukusebenzisa ifom yePythagoras, sifumana:

AV² = АД² + ВД²

Emva kokuba uzimisele ukusuka kwi-VD ibinzana kwaye ubeka endaweni yesaziso esasetyenziswa ngaphambili, siyafumana:

² = = ² - (в / 2) ².

Kubalulekile ukukhupha ingcambu:

H = √a² - ngo -² / 4.

Ukuba siphumela kumqondiso weengcambu ¼, i-formula iya kubonakala ngathi:

H = ½ √4a² - ngo -².

Oku kukuphakama kwixantathu ye-isosceles. Ifom elandelayo ivela kwi-theorem yasePythagoras. Nangona ulibale le yokungena, ngoko, ukwazi indlela yokufumana, unako ukuwususa.

Ukuphakama kwefomula 2

Ifom echazwe ngasentla yintloko kwaye isetyenziswa rhoqo ekuxazululeni iingxaki ezininzi zeJometri. Kodwa akayena kuphela. Ngamanye amaxesha kwimeko, endaweni yesiseko, ixabiso le-angle linikezelwa. Ngaloo datha, indlela yokufumana ukuphakama kwincantathu ye-isosceles? Ukujongana neengxaki ezifanayo kuyacetyiswa ukusebenzisa ifom ehlukile:

H = a / isono α,

Uphi u-H ubude obujoliswe kwisiseko,

Kodwa-icala,

I-Α iyona ngqangi kwisiseko.

Ukuba umsebenzi unika ixabiso le-angle kwi-vertex, ngoko ukuphakama kwinqantathu ye-isosceles kulandelayo:

H = a / cos (β / 2),

Uphi uH ubuphakamileyo bubunxweme,

I-B iyona ngqungquthela kwi-vertex,

Kwaye-kwicala.

Unxantathu we-isosceles

Ipropati enomdla kakhulu unxantathu, i-vertex yayo i-degrees 90. Cinga unxantathu ochanekileyo ABC. Njengamaxesha adlulileyo, i-VD yindawo ephakamileyo ekujoliswe kuyo.

Iibangele kwisiseko zilingana. Bala umsebenzi wabo omkhulu awuyi kuba:

Α = (180-90) / 2.

Ngako oko, ii-angles kwisiseko zihlala zihlala kuma-degrees ama-45. Khawucinge ngxantathu ye-ADV. Kwakhona ixande. Makhe sifumane i-angle ye-ABD. Ngezibalo ezilula, sifumana ama-45 degrees. Kwaye, ngenxa yoko, le nxantathu ayikho nje ingxande, kodwa i-isosceles. Amaqela AD kunye ne-VD ngamacala angamazantsi kwaye alinganayo phakathi kwabo.

Kodwa icala leBP ngexesha elifanayo liyingxenye yecala le-AC. Kubonakala ukuba ukuphakama kwincantathu ye-isosceles kuyisiqingatha sesiseko, kwaye ukuba kubhalwe kwifom yefomula, sithobela eli lilandelayo:

H = B / 2.

Kufuneka kukhunjulwe ukuba le fomyula yimeko ekhethekileyo, kwaye ingasetyenziselwa kuphela ii-triangles ze-isosceles ezixandekileyo.

I triangles zegolide

Unomdla kakhulu unxantathu wegolide. Kule nani, umlinganiselo wesalathisi kwisiseko silingana nexabiso elibizwa ngokuba yinombolo ye Phidias. I-angle engentla i-degrees ezingama-36, kwisiseko-72 degrees. Le nxantathu yayithandwa yiPythagore. Imigaqo yexantathu yegolide isiseko sezinto ezininzi ezingapheliyo. Eyaziwa kuzo zonke iinkwenkwezi ezinamahlanu ezinokwakheka zakhiwe kwintlupheko ye-isosceles triangles. Kwizinto ezininzi ezidalwa, uLeonardo da Vinci wasebenzisa umgaqo "wexantathu yegolide". Ukubunjwa "i-Gioconda" kusekelwe ngokuchanekileyo kwimifanekiso eyenza inkwenkwezi rhoqo.

Umfanekiso "UCubism", enye yezinto ezidaliweyo zikaPablo Picasso, uyamthabatha imbono esekelwe kwisigxathu se-isosceles.