Khatisong ena, re tla hlahloba e 'ngoe ea likhopolo-taba tsa Euclidean geometry - theorem ea Stewart, e ileng ea fumana lebitso le joalo ho tlotla setsebi sa lipalo sa Lenyesemane M. Stewart, ea ileng a paka. Hape re tla sekaseka ka ho qaqileng mohlala oa ho rarolla bothata ho kopanya boitsebiso bo hlahisitsoeng.
Polelo ea theorem
Dan triangolo ABC. Ka lehlakoreng la hae AC ntlha e nkuweng D, e hokahaneng le holimo B. Re amohela molaetsa o latelang:
- AB = a
- BC = b
- BD = leq
- AD = x
- DC = le
Ho kgutlotharo ena, tekano ke nnete:
Tšebeliso ea theorem
Ho tsoa ho theorem ea Stewart, liforomo li ka fumanoa bakeng sa ho fumana li-medians le li-bisectors tsa triangle:
1. Bolelele ba karolo e 'meli
A lc ke sethako se hoheloa ka lehlakore c, e arotsoeng ka likarolo x и y. Ha re nke mahlakoreng a mang a mabeli a kgutlotharo e le a и b… Boemong bona:
2. Bolelele ba bohareng
A mc ke mahareng a theotsoe ka thoko c. Ha re boleleng mahlakore a mang a mabeli a kgutlotharo e le a и b… Joale:
Mohlala oa bothata
Triangle e fanoeng ABC. Ka lehlakoreng AC e lekana le 9 cm, ntlha e nkuweng D, e arolang lehlakore hore AD bolelele habedi DC. Bolelele ba karolo e kopanyang vertex B le ntlha Dbolelele, 5 cm. Tabeng ena, kgutlotharo e entsoeng US ke isosceles. Fumana mahlakore a setseng a kgutlotharo ABC.
tharollo
Ha re bonts'e maemo a bothata ka mokhoa oa ho taka.
AC = AD + DC = 9cm. AD nako e telele DC habeli, ke hore AD = 2DC.
Ka hona, 2DC + DC = 3DC 9d XNUMX cm. Kahoo, DC = 3cm, AD = 6cm.
Hobane kgutlotharo US - li-isosceles, le lehlakore AD ke 6 cm, kahoo ba lekana AB и BDIe AB = 5cm.
E sala feela ho fumana BC, ho tsoa ho theorem ea Stewart:
Re kenya litekanyetso tse tsejoang sebakeng sa polelo ena:
Ka tsela ena, BC = √52 ≈ 7,21 cm.