Okuqukethwe
Kule ncwadi, sizocubungula enye yezindlela zakudala ze-affine geometry - i-Ceva theorem, eyathola igama elinjalo ngokuhlonipha unjiniyela wase-Italy u-Giovanni Ceva. Sizophinde sihlaziye isibonelo sokuxazulula inkinga ukuze sihlanganise indaba ethulwayo.
Isitatimende sethiyori
Unxantathu unikiwe ABC, lapho i-vertex ngayinye ixhunywe khona endaweni ephambene.
Ngakho, sithola izingxenye ezintathu (AA', BB' и CC'), ababizwa cevians.
Lezi zingxenye ziyaphambana ngesikhathi esisodwa uma futhi kuphela uma ukulingana okulandelayo kubamba:
|KANYE'| | | |HHAYI'| | | |CB'| = |BC'| | | |SHIFT'| | | |AB'|
I-theorem ingaphinde yethulwe kuleli fomu (kunqunywa ukuthi amaphuzu ahlukanisa izinhlangothi ngasiphi isilinganiso):
Ithiyori ye-trigonometric kaCeva
Qaphela: wonke amakhona aqondile.
Isibonelo senkinga
Unxantathu unikiwe ABC ngamachashazi KUYA', B' и VS ' emaceleni BC, AC и AB, ngokulandelana. Ama-vertices kanxantathu axhunywe emaphuzwini anikeziwe, futhi izingxenye ezakhiwe zidlula iphuzu elilodwa. Ngesikhathi esifanayo, amaphuzu KUYA' и B' kuthathwe emaphoyinti aphakathi ezinhlangothini ezibhekene ezihambisanayo. Thola ukuthi iphuzu likusiphi isilinganiso VS ' ihlukanisa uhlangothi AB.
Isixazululo
Ake sidwebe umdwebo ngokwezimo zenkinga. Ukuze kube lula ngathi, samukela lesi saziso esilandelayo:
- AB' = B'C = a
- BA' = A'C = b
Kusele kuphela ukuhlanganisa isilinganiso sezigaba ngokuya ngethiyori ye-Ceva bese ufaka esikhundleni senothi eyamukelwe kuyo:
Ngemuva kokunciphisa ama-fractions, sithola:
Ngakho, AC' = C'B, okungukuthi iphuzu VS ' ihlukanisa uhlangothi AB phakathi.
Ngakho-ke, kunxantathu wethu, izingxenye AA', BB' и CC' bangabaphakathi. Ngemva kokuxazulula inkinga, sibonise ukuthi ziyaphambana ngesikhathi esisodwa (zivumelekile kunoma yimuphi unxantathu).
Qaphela: usebenzisa i-theorem kaCeva, umuntu angafakazela ukuthi kunxantathu ngesikhathi esisodwa, ama-bisectors noma ukuphakama nakho kuyaphambana.