Indlela ukuthola uhlangothi unxantathu kwesokudla? Basics of geometry

Imilenze kanye hypotenuse - ohlangothini unxantathu kwesokudla. Okokuqala - lokhu kumasegmenti ukuthi kukhona ezakhelene engela kwesokudla kanye hypotenuse ingxenye ende kunazo zonke sibalo futhi okuphambene engela ^90. unxantathu Pythagorean libizwa ohlangothini omunye okuyizinto izinombolo yemvelo; ubude bawo kulokhu abizwa ngokuthi "kathathu Pythagorean".

unxantathu waseGibhithe

Ukuze isizukulwane samanje uye wafunda geometry ngesimo lapho ngoba siyafundwa esikoleni manje, uye wazakhela emakhulwini ambalwa eminyaka. Kuthathwa siyinhloko theorem kaPythagoras. uhlangothi kukanxande ka unxantathu (figure is emhlabeni wonke ezaziwa) kukhona 3, 4, 5.

Bambalwa abangalwazi ngamazwi athi "ibhulukwe Pythagorean kuzo zonke izinhlangothi bayalingana." Kodwa eqinisweni, Theorem umsindo kube: c ² (esigcawini hypotenuse) = ² + b ² (isamba sezikwele imilenze).

Phakathi zezibalo calantsatfu izinhlangothi 3, 4, 5 (bheka, m r. D.) Ingabe "waseGibhithe '. Kuyathakazelisa ukuthi engaba umbuthano olotshwe sibalo lingana kuze fike. Igama kwathi ngekhulu V BC, lapho zefilosofi waya eGibhithe.

Lapho wokwakha abaklami iphiramidi kanye abahloli zisebenzisa isilinganiso 3: 4: 5. Lezi zakhiwo ukuthola yakheke, enhle ebukeka futhi ivulekile, futhi kuyaqabukela ngiyaquleka.

Ukuze kwakhiwe engela kwesokudla, abakhi wasebenzisa intambo lapho engeyokuqala 12 iye abethela. Kulokhu, ematfuba wokwakha unxantathu wesokudla luyanda 95%.

Izimpawu ukulingana izibalo

• I-engeli acute ngendlela unxantathu kwesokudla kanye nohlangothi esikhulu okuyinto ilingana zakhi unxantathu yesibili, - uphawu obungenakuphikwa kokulingana izibalo. Ikhumbula inani engeli, kulula ukuze afakazele ukuthi engeli yesibili acute nazo alinganayo. Ngakho, aboncantathu Bayefana isici sesibili.
• Lapho isicelo izingcezu ezimbili kwa each nye uphendukisa kubo ukuze niyafanelana, ziye zaba enye unxantathu isosceles. Ngokusho impahla amaqembu, noma kunalokho, hypotenuse ilingana, kanye nama-engeli ngasesinqeni, ngakho lezi zibalo ziyafana.

Ngokusho isici sokuqala-ke kulula kakhulu ukuqinisekisa ukuthi onxantathu ngempela alinganayo, inqobo nje uma la maqembu amabili amancane (isb. E. imilenze) ayalingana nomunye.

Triangles ayafana ngesisekelo II, essence itholakala kwesibalo emlenzeni engela oyingozi.

Izakhiwo unxantathu nge engela kwesokudla

Ukuphakama, okuyinto yehliselwa angle kwesokudla, uhlukanisa isibalo izingxenye ezimbili alinganayo.

La maqembu unxantathu kwesokudla futhi aphansi namaphakathi kwalo kalula obonwa umthetho: imidiyeni, okuyinto uhlezi phezu hypotenuse uyalingana ingxenye yako. Umumo Square kungatholakala kokubili lwefomula le Heron, futhi isiqinisekiso ukuthi ulingana isigamu umkhiqizo nezinye izinhlangothi ezimbili.

I izici angled unxantathu engeli 30 ^o, 45 ^o 60 ^o.

• Engela, okuyinto ilingana ^angu-30, kufanele sikhumbule ukuthi ophikisayo kuyoba ulingana 1/2 beqembu elikhulu.
• Uma engela ⁴⁵ °, ngakho-engeli yesibili acute kubuye ⁴⁵ °. Lokhu kusikisela ukuthi unxantathu kuyinto isosceles futhi imilenze yayo bayalingana.
• Impahla ye-engeli ⁶⁰ itholakala lokuthi angle third-degree has a ^elithile 30.

Le ndawo kalula owaziwa omunye amafomula ezintathu:

1. ngokusebenzisa ukuphakama futhi ohlangothini lapho uwe;
2. ifomula Heron sika;
3. ezinhlangothini futhi igebe eliphakathi kwabo.

La maqembu unxantathu kwesokudla, noma kunalokho imilenze bukhomba ku eziphakeme ezimbili ezihlukene. Ukuze uthole lwesithathu, kubalulekile ukuba sicabangele unxantathu okuholela, bese theorem kaPythagoras ukubala ubude okudingekayo. Ngaphezu kule formula kukhona kabili isilinganiso endaweni futhi ubude hypotenuse. Inkulumo ezivamile phakathi abafundi owokuqala, ngoba kudinga izibalo ambalwa.

Theorem isetshenziswa unxantathu kwesokudla

kwesokudla unxantathu geometry kuhlanganisa nokusetshenziswa theorems ezifana:

1. ifayela echaza ifomu Pythagorean. essence yayo itholakala iqiniso ukuthi esigcawini hypotenuse lilingana isamba izigcawu the nezinye izinhlangothi ezimbili. Ngo-geometry Euclidean, lokhu isilinganiso kuyisihluthulelo. Sebenzisa ifomula kungenzeka, uma benikwe unxantathu, isibonelo, SNH. SN - the hypotenuse, futhi kubalulekile ukuthola. Khona-ke SN ² = NH ² + HS ^2.
2. Cosine theorem. Finqa theorem kaPythagoras: g ² = f ² + s ² -2fs * cos engela therebetween. Ngokwesibonelo, uma unikezwe unxantathu DOB. DB umlenze eyaziwa futhi hypotenuse DO, kumele uthole OB. Khona-ke ifomula kuthatha ifomu: OB ^{2 2} = DB + DO ² -2DB * DO * cos engela D. Kukhona nemiphumela ezintathu: ekhoneni acute-yomumo unxantathu ukuthi, uma isamba sezikwele sezinhlangothini zombili ze-isikwele ukhupha obuphelele lwesithathu, umphumela kumelwe ibe ngaphansi kuka-zero. Angle - obtuse, ukube bekunjalo, uma le nkulumo ngaphezu kuka-zero. Angle - umugqa oholayo.
3. ifayela echaza ifomu Sine. Ukhombisa ubudlelwano phakathi kwezinhlangano zentando emagumbini aphikisanayo. Ngamanye amazwi, isilinganiso ubude ezinhlangothini ezihlukene ukuze sine ye-engeli. Ngo unxantathu HFB, lapho hypotenuse kuyinto hf, ke kuyoba yiqiniso: hf / isono engela B = FB / isono engela H = HB / isono engela F.