Tse ka Hare
Khatisong ena, re tla tšohla e 'ngoe ea li-theorems tsa khale tsa affine geometry - theorem ea Ceva, e ileng ea fumana lebitso le joalo ho tlotla moenjiniere oa Motaliana Giovanni Ceva. Re tla boela re hlahlobe mohlala oa ho rarolla bothata e le ho kopanya boitsebiso bo fanoeng.
Polelo ea theorem
Triangle e fanoeng ABC, moo vertex e 'ngoe le e 'ngoe e hokahaneng le ntlha e ka lehlakoreng le leng.
Kahoo, re fumana likarolo tse tharo (AA', BB' и CC'), tse bitsoang cevians.
Likarolo tsena li kopana ka nako e le 'ngoe haeba feela tekano e latelang e tšoarella:
|LE'| |NO'| |CB'| = |BC'| |SHIFT'| |AB'|
Theorem e ka boela ea hlahisoa ka mokhoa ona (ho khethoa hore na lintlha li arola mahlakoreng ka karolelano efe):
Ceva's trigonometric theorem
Tlhokomeliso: likhutlo tsohle li sekametse.
Mohlala oa bothata
Triangle e fanoeng ABC e nang le matheba HO', B и VS ' mahlakoreng BC, AC и AB, ka ho latellana. Li-vertices tsa khutlo-tharo li hokahane le lintlha tse fanoeng, 'me likarolo tse entsoeng li feta ntlha e le' ngoe. Ka nako e ts'oanang, lintlha HO' и B e nkuweng bohareng ba mahlakore a tshoanang a fapaneng. Fumana hore na ntlha e kae VS ' e arola lehlakore AB.
tharollo
A re takang setšoantšo ho latela maemo a bothata. Bakeng sa boiketlo ba rona, re amohela molaetsa o latelang:
- AB' = B'C = a
- BA' = A'C = b
E sala feela ho theha karo-karolelano ea likarolo ho ea ka theorem ea Ceva le ho kenya lengolo le amohelehang ho eona:
Ka mor'a ho fokotsa likaroloana, re fumana:
Kahoo, AC' = C'B, ke hore ntlha VS ' e arola lehlakore AB ka halofo.
Ka hona, ka triangolo ea rona, likarolo AA', BB' и CC' ke ba mahareng. Ha re se re rarolotse bothata, re ile ra paka hore li kopana ka nako e le 'ngoe (li sebetsa bakeng sa khutlotharo efe kapa efe).
Hlokomela: ho sebelisa theorem ea Ceva, motho a ka paka hore ka khutlo-tharo ka nako e 'ngoe, li-bisectors kapa bophahamo le tsona lia kopana.