M'bukuli, tiwona imodzi mwamalingaliro akulu a Euclidean geometry - theorem ya Stewart, yomwe idalandira dzina lotere polemekeza katswiri wa masamu wachingerezi M. Stewart, yemwe adatsimikizira. Tidzasanthulanso mwatsatanetsatane chitsanzo chothetsera vutoli kuti tiphatikize zomwe zaperekedwa.
Chidziwitso cha theorem
Dan katatu ABC. Pambali pake AC mfundo yatengedwa D, yomwe imagwirizanitsidwa pamwamba B. Timavomereza mawu awa:
- AB = a
- BC = b
- BD = p
- AD = x
- DC = ndi
Kwa makona atatu awa, kufanana ndi zoona:
Kugwiritsa ntchito theorem
Kuchokera ku theorem ya Stewart, mafomu angatengedwe kuti apeze apakati ndi ma bisectors a katatu:
1. Kutalika kwa bisector
Tiyeni lc ndi bisector yokokedwa kumbali c, yomwe imagawidwa m'magulu x и y. Tiyeni titenge mbali zina ziwiri za makona atatu ngati a и b… Pamenepa:
2. Utali wapakati
Tiyeni mc ndiye wapakati watembenuzidwira mbali c. Tiyeni tiwone mbali zina ziwiri za makona atatu ngati a и b… Kenako:
Chitsanzo cha vuto
Triangle yapatsidwa ABC. Kumbali AC yofanana ndi 9cm, mfundo yatengedwa D, zomwe zimagawaniza mbali kuti AD kawiri kutalika DC. Kutalika kwa gawo lolumikiza vertex B ndi mfundo D,ndi 5cm. Pankhaniyi, anapanga makona atatu US ndi isosceles. Pezani mbali zotsalira za makona atatu ABC.
Anakonza
Tiyeni tiwonetse momwe vutolo lilili muzojambula.
AC = AD + DC = 9 masentimita. AD yaitali DC kawiri, ie AD = 2DC.
Zotsatira zake, 2DC + DC = 3DC 9d XNUMX cm. Choncho, DC = 3cm, AD = 6 masentimita.
Chifukwa katatu US - isosceles, ndi mbali AD ndi 6 cm, choncho ndi ofanana AB и BDIe AB = 5 masentimita.
Zimangokhala kupeza BC, kuchokera ku chiphunzitso cha Stewart:
Timalowetsa zikhalidwe zodziwika m'mawu awa:
Mwa njira iyi, BC = √52 ≈ 7,21 cm.