Kutalika kwa makona atatu

M'bukuli, tikambirana zautali wautali mu makona atatu oyenera, komanso kusanthula zitsanzo zothetsera mavuto pamutuwu.

Zindikirani: makona atatu amatchedwa amakona atatu, ngati imodzi mwa ngodya zake ili yolondola (yofanana ndi 90 °) ndipo ena awiri ndi ovuta (<90 °).

Utali katundu mu makona atatu kumanja

Katundu 1

Makona atatu kumanja ali ndi utali wautali (h₁ и h₂) zimagwirizana ndi miyendo yake.

utali wachitatu (h₃) amatsikira ku hypotenuse kuchokera kumbali yoyenera.

Katundu 2

Malo a orthocenter (malo olowera utali) a makona atatu akumanja ali pa vertex ya ngodya yolondola.

Katundu 3

Kutalika kwa makona atatu kumanja komwe kumakokedwa ku hypotenuse kumagawaniza mu makona atatu ofanana kumanja, omwe alinso ofanana ndi oyambirirawo.

1. △US ~ △ABC pa ngodya ziwiri zofanana: ∠ADB = ∠LAC (mizere yowongoka), ∠US = ∠ABC.

2. △ADC ~ △ABC pa ngodya ziwiri zofanana: ∠ADC = ∠LAC (mizere yowongoka), ∠Zamgululi = ∠ACB.

3. △US ~ △ADC pa ngodya ziwiri zofanana: ∠US = ∠DAC, ∠OIPA = ∠Zamgululi.

Umboni: ∠OIPA = 90° – ∠ABD (ABC). Nthawi yomweyo ∠ACD (ACB) = 90° – ∠ABC.

Chifukwa chake, ∠OIPA = ∠Zamgululi.

Zitha kutsimikiziridwa chimodzimodzi kuti ∠US = ∠DAC.

Katundu 4

Mu makona atatu kumanja, kutalika kokokera ku hypotenuse kumawerengedwa motere:

1. Kupyolera mu zigawo za hypotenuse, opangidwa chifukwa cha kugawanika kwake ndi maziko a msinkhu:

2. Kupyolera mu utali wa mbali za makona atatu:

Fomula iyi idachokera ku Katundu wa sine wa ngodya pachimake mu makona atatu kumanja (sine wa ngodya ndi wofanana ndi chiŵerengero cha mwendo wosiyana ndi hypotenuse):

Zindikirani: ku makona atatu akumanja, kutalika kwake komwe kumaperekedwa m'mabuku athu - kumagwiranso ntchito.

Chitsanzo cha vuto

Ntchito 1

The hypotenuse ya makona atatu kumanja amagawidwa ndi kutalika komwe amakokedwerako mu magawo 5 ndi 13 cm. Pezani kutalika kwa kutalika uku.

Anakonza

Tiyeni tigwiritse ntchito fomula yoyamba yomwe yaperekedwa Katundu 4:

Ntchito 2

Miyendo ya makona atatu akumanja ndi 9 ndi 12 cm. Pezani kutalika kwa kutalika komwe kukopedwa ndi hypotenuse.

Anakonza

Choyamba, tiyeni tipeze kutalika kwa hypotenuse pamodzi (lole miyendo ya makona atatu ikhale "ku" и "B", ndi hypotenuse ndi "vs"):

c² =A² + b² = 9² + 12² = 225.

Zotsatira zake, с = 15 masentimita.

Tsopano titha kugwiritsa ntchito chilinganizo chachiwiri kuchokera Katundu 4zafotokozedwa pamwambapa: