Indlela yokuthola ukuphakama unxantathu equilateral? Formula indawo, ukuphakama izakhiwo unxantathu equilateral

Jiyomethri - akusiwona nje sifundvo lesisemtsetfweni lapho udinga ukuthola amaphuzu aphelele. Libuye libe nolwazi ukuthi ngokuvamile kudingeka empilweni. Ngokwesibonelo, lapho indlu enophahla okusezingeni eliphezulu kuyadingeka ukubala ukushuba we izingodo kanye nenombolo yabo. Kulula uma wazi kanjani ukuthola ukuphakama unxantathu equilateral. izakhiwo zasendulo zisekelwe ulwazi property izibalo weJiyomethri. Letinhlobo izakhiwo zivame zibukeke zifane nabo. Imibhoshongo yaseGibithe, obisi, efekethisiwe kwezobuciko, enyakatho imidwebo ngisho amakhekhe - zonke onxantathu ezungeze umuntu. Njengoba uPlato akusho, umhlaba wonke kusekelwe onxantathu.

unxantathu isosceles

Ukuze wenze kube sobala, njengoba uzobe kuchazwe lapha ngentasi, kuwufanele kancane ukukhumbula izinto eziyisisekelo geometry.

Unxantathu kuyinto isosceles uma kukabili alinganayo. Babehlale shayela uhlangothi. Party kabani Ubukhulu kuhluke, ezibizwa ngokuthi yizisekelo.

imiqondo eyisisekelo

Njenganoma yimuphi isayensi, i-geometry inezidingo imithetho yayo eziyisisekelo futhi imiqondo. Iningi labo. Cabanga labo kuphela ngaphandle okuyinto isihloko sethu izoke akucacile.

Ukuphakama - lena umugqa oqondile ungenisa perpendicular uhlangothi.

Median - ingxenye iqondiswe kusukela vertex unxantathu ngamunye kuphela phakathi uhlangothi.

Bisector - ugodo ehlukanisa ngesigamu engela.

Bisector unxantathu - it is a ngqo, noma kunalokho, ingxenye bisector, yokuxhuma phezulu uhlangothi.

Kubalulekile ukukhumbula ukuthi i-bisector ye-engeli - kuba ray eyisibopho kanye unxantathu bisector - ingxenye ugongolo.

Kumila engeli we

Theorem lithi emakhoneni zitholakala ngasesinqeni se iyiphi unxantathu isosceles zihlale alinganayo. Ukuze afakazele lokhu theorem silula. Cabanga kuboniswe unxantathu isosceles ABC, lapho AB = BC. Kusukela ABC bisector engela ezidingekayo HP. Manje unxantathu ezimbili okuholela kufanele kubhekwe. On isimo AB = BC, HP ohlangothini onxantathu bebonke, futhi engele AED kanye Kusho ukuthini ukuba umKristu bayalingana, ngoba vd - bisector. Ukukhumbula kuqubuka ukulingana, singaphetha kahle ngokuthi aboncantathu ezibhekwa alinganayo. Ngenxa yalokho, yonke engele olufanele bayalingana. Futhi-ke, amaqembu, kodwa ngaleso sikhathi kuyoba abuye kamuva.

Ukuphakama unxantathu isosceles

Theorem ayisisekelo, ogxile isixazululo cishe zonke imisebenzi, yilesi: ukuphakama ngaphakathi unxantathu equilateral iyona bisector futhi aphansi namaphakathi. Sibuqonde salo esisebenzayo (noma i-essence) kufanele wenze ukwesekwa nesabelo. Ukuze wenze lokhu, usike iphepha isosceles unxantathu. Indlela elula yokwenza lokhu kusukela ishidi ajwayelekile notebook ebhokisini.

Songa unxantathu okuholela nengxenye, bakubheka ezinhlangothini. Kwenzekeni? onxantathu amabili alinganayo. Manje hlola izibikezelo. Nweba origami okuholela. Dweba umugqa aphindekile. Nge protractor hlola igebe eliphakathi umugqa ezaziqoshwe futhi isisekelo unxantathu. Yini engela 90 degrees? Iqiniso ukuthi ulayini besondele - perpendicular. Ngu definition - ukuphakama. Indlela yokuthola ukuphakama unxantathu equilateral, siye waqonda. Manje amagumbi phezulu. Ukusebenzisa okufanayo isheke protractor engeli, manje kwakhiwa kakade okusezingeni eliphezulu. Bayalingana. Lokhu kusho ukuthi ukuphakama kokubili bisector. Ehlome umbusi, ukukala kumasegmenti kulo ukuphakama base. Bayalingana. Ngenxa yalokho, ubude e unxantathu equilateral bisects base futhi kuyinto aphansi namaphakathi.

ubufakazi

Izinsiza-kufundisa ubonisa ngokucacile ukuthi akhona ubuqiniso theorem. Kodwa-geometry - isayensi olunembile ngokwanele, ngakho kuyabonakala namanje.

Phakathi kokucubungula nokulingana engeli ngasesinqeni lalingakufanelekele onxantathu alinganayo. Khumbula, WA - bisector, kanye onxantathu AED kanye Kusho ukuthini ukuba umKristu bayalingana. Isiphetho kwaba ukuthi izinhlangothi elihambisana unxantathu futhi, yebo, engele bayalingana. Ngakho AD = SD. Ngenxa yalokho, WA - lesemkhatsini. It uhlala ukufakazela ukuthi HP kuphezulu. Ngokusekelwe nokulingana onxantathu ukucabangela, kuvela ukuthi engela ilingane ADD engela ADV. Kodwa lezi engeli amabili kukhona eduze futhi aye abonakala ukungenza 180 degrees. Ngakho-ke, lokho abayikho? Yiqiniso, ngo-90 degrees. Ngakho, HP - ukuphakama e unxantathu equilateral badonsekela base. QED.

imphawu letibalulekile

• Ukuze babhekane nezinselele, kufanele sikhumbule izici eziyinhloko isosceles onxantathu. Babonakala theorem ephambene.
• Uma ngokuhamba yokuxazulula le nkinga iyabheda ukutholwa nokulingana engeli amabili, kusho ukuthi wena obhekana nakho unxantathu isosceles.
• Uma ungakwazi ukufakazela ukuthi imidiyeni futhi ukuphakama unxantathu, ngokuphepha buyela - unxantathu kuyinto isosceles.
• Uma bisector ukuphakama-ke, ngokusekelwe izici eziyinhloko unxantathu wabhekisela unxantathu isosceles.
• Futhi-ke, uma imidiyeni futhi ukhonza njengesisebenzi ukuphakama, unxantathu ezinjalo - isosceles.

ukuphakama Formula 1

Nokho, ukuze ukwazi ukuhlangabezana nemisebenzi kakhulu, kudingeka sithole izibalo ukuphakama value. Yingakho sicabanga ukuthi ungathola kanjani ukuphakama unxantathu equilateral.

Ukubuyela sibalo ngenhla, ABC, lapho - hlangothi - isizinda. HP - ukuphakama unxantathu, it has uphawu h.

Kuyini unxantathu AED? Njengoba HP - ukuphakama ke unxantathu AED - umlenze wamaqhuqhuva ukuthi ufuna ukuthola. Ukusebenzisa ifomula Pythagorean, sithola:

= + AV² AD² VD²

Belinganisa vd inkulumo futhi abambele abizwa yokutholwa ngaphambili, sithola:

N² = a² - (a / 2) ².

Kufanele ususe impande:

H = √a² - v² / 4.

Uma wenza ¼ isibonakaliso impande ke ifomula kungaba:

H = ½ √4a² - v².

Unjalo ubude unxantathu equilateral. Ifomula ethathwe theorem kaPythagoras. Ngisho noma thina ukhohlwe notation ongokomfanekiso-ke, uma wazi ukuthi indlela ayekutholile, ungahlala nililethe.

ukuphakama ifomula 2

Ifomula ezichazwe ngenhla okuyisisekelo kanye ngokuvamile ezisetshenziswa ezindaweni eziningi izinkinga yejeyomethri. Kepha kabanga kuphela. Ngezinye izikhathi enikeziwe esikhundleni base ukubaluleka engeli enikeziwe. Lapho idatha efana ukuthola ukuphakama unxantathu equilateral? Ukuze kuxazululwe lezi zinkinga kungcono ukusebenzisa ifomula ezahlukene:

H = a / isono α,

lapho H - ukuphakama, ubheke phansi,

futhi - nohlangothi lateral,

α - engela ngasesinqeni.

Uma inkinga unikezwa engela ngesikhathi vertex, ukuphakama ngaphakathi unxantathu equilateral simiswe ngalendlela lelandzelako:

H = a / cos (β / 2),

lapho H - ukuphakama, sehliselwe base ,,

β - i-engeli ngesikhathi sokudlondlobala,

futhi - izinhlangothi.

Kwesokudla unxantathu isosceles

impahla Very interesting has a unxantathu, beyizidalwa eziphakeme kunazo zonke okuyinto ilingana 90 degrees. Cabangela unxantathu wesokudla-angled ABC. Njengoba ezimweni langaphambilini, WA - ukuphakama ngase base.

I-engeli base bayalingana. Bala umsebenzi wabo omkhulu ngeke wenze:

α = (180 - 90) / 2.

Ngakho, emakhoneni sise isizinda, njalo 45 degrees. Manje cabanga ADV unxantathu. Wabuye kuyinto unxande. Sithola AED engela. Ngu izibalo ezilula sithola degrees 45. Futhi, ngakho-ke, lokhu unxantathu akulungile kuphela, kodwa futhi isosceles. La maqembu AD futhi vd kukhona izinhlangothi futhi bayalingana.

Kodwa ohlangothini AD ngesikhathi esifanayo uhhafu-AU. It kuvela ukuthi akakho ekuphakameni unxantathu equilateral ilingana isigamu base, sengathi yalotshwa njengezingoma zohlobo oluthile yefomula, sithola amazwi athi elandelayo:

H = a / 2.

Kufanele kukhunjulwe ukuthi lesi ifomula kuphela uma ekhethekile, futhi ingasetshenziswa kuphela unxande onxantathu isosceles.

Golden unxantathu

Very interesting kuyinto unxantathu segolide. Kulesi sibalo, isilinganiso ohlangothini base ilingana nenani, ngokuthi isibalo Phidias. Corner elise phezulu - degrees 36, ne-base - 72 degrees. Lokhu unxantathu bayahlonishwa Pythagoreans. izimiso yeGolden Triangle yisisekelo sebuningini yobuciko ongafi. I owaziwa inkanyezi ezinhlanu enamaphoyinti eyakhelwe ezimpambanweni zomgwaqo onxantathu isosceles. Emisebenzini eminingi uLeonardo da Vinci wasebenzisa isimiso "unxantathu osemqoka". Ukwakheka "Mona Lisa" kusekelwe nje izibalo, okuyinto ukudala Pentagram kwesokudla.

Ukudweba "Cubism", omunye Pablo Pikasso usebenza, buka elithakazelisayo yakha isisekelo unxantathu isosceles.