M'buku lino, tikambirana imodzi mwa ziphunzitso zakale za affine geometry - chiphunzitso cha Ceva, chomwe chinalandira dzina lotere polemekeza injiniya wa ku Italy Giovanni Ceva. Tidzasanthulanso chitsanzo cha kuthetsa vutolo kuti tiphatikize mfundo zomwe zaperekedwa.
Chidziwitso cha theorem
Triangle yapatsidwa ABC, momwe vertex iliyonse imalumikizidwa ndi mfundo ya mbali ina.
Chifukwa chake, timapeza magawo atatu (AA', BB' и CC'), omwe amatchedwa cevians.
Magawo awa amadutsana nthawi imodzi pokhapokha ngati izi zili ndi zofanana:
|NDI'| | | |OSATI'| | | |CB'| | = |BC'| | | |SHIFT'| | | |AB'|
Theorem ingathenso kufotokozedwa mu mawonekedwe awa (amatsimikiziridwa mu chiŵerengero chomwe mfundozo zimagawaniza mbalizo):
Ceva's trigonometric theorem
Zindikirani: ngodya zonse ndi zolunjika.
Chitsanzo cha vuto
Triangle yapatsidwa ABC ndi madontho KWA', B' и C' kumbali BC, AC и AB, motero. Ma vertices a makona atatu amalumikizidwa ndi mfundo zomwe zaperekedwa, ndipo magawo opangidwa amadutsa mfundo imodzi. Pa nthawi yomweyo, mfundo KWA' и B' kutengedwa pakati pa mbali zofananira. Pezani mu chiŵerengero cha mfundo C' amagawaniza mbali AB.
Anakonza
Tiyeni tijambule chojambula molingana ndi momwe vutolo lilili. Kuti zitithandize, timatsatira mfundo zotsatirazi:
- AB = B'C = a
- BA = A'C = b
Zimangotsala kupanga chiŵerengero cha zigawo molingana ndi chiphunzitso cha Ceva ndikulowetsamo mawu ovomerezeka:
Pambuyo kuchepetsa magawo, timapeza:
Choncho, AC' = C'B, ie point C' amagawaniza mbali AB pakati.
Choncho, mu makona atatu athu, zigawo AA', BB' и CC' ndi amkatikati. Titathetsa vutoli, tidatsimikizira kuti amadutsa nthawi imodzi (yovomerezeka pamakona atatu aliwonse).
Zindikirani: pogwiritsa ntchito chiphunzitso cha Ceva, munthu akhoza kutsimikizira kuti mu makona atatu panthawi imodzi, ma bisectors kapena kutalika kwake kumadutsanso.