Indlela ukufumana icala kanxantathu sokunene? Basics we geometry

Imilenze kunye hypotenuse - ecaleni kanxantathu tye. Okokuqala - oku inxalenye ukuba ezikufutshane ukuya kwikona yelayini esuka ekunene kwaye hypotenuse na inxalenye lide mzobo yaye malunga engile ^90. unxantathu kaPythagoras kuthiwa icala elinye lawo la amanani zendalo; ubude yabo kulo mzekelo zibizwa ngokuba "kathathu kaPythagoras".

unxantathu Egyptian

Ukuya sizukulwana uye wafunda geometry ngendlela apho kufundiswa kwisikolo ngoku, iye yaphuhliswa kwiinkulungwane eziliqela. Kucingwa sibalulekile theorem kaPythagoras. kwicala ezizingxande kanxantathu (inani esaziwa ehlabathini liphela) ezi-3, 4, 5.

Bambalwa abangekho uqhelene ibinzana elithi "iblukhwe kaPythagoras kuwo onke amacala bayalingana." Kodwa enyanisweni, theorem izandi kuba: c ² (isikweri hypotenuse) = ² + b ² (udibaniso lwezikweri imilenze).

Phakathi zezibalo unxantathu macala 3, 4, 5 (bona, m kunye r. D.) Ngaba 'baseYiputa'. Loo nto inika umdla radius wesangqa ubhalwe ngokomzekeliso esilingana omnye. Igama Kwathi ngenkulungwane V BC, xa zobulumko zamaGrike waya eYiputa.

Xa kusakhiwa abakhi iphiramidi kunye abahloli basebenzisa ratio ye-3: 4: 5. La maziko bafumana yakheke, nice ngenkangeleko kwaye eliphangaleleyo, yaye kunqabile inciphisiwe.

Ukuze ukwakha esinekona sasekunene, abakhi basebenzisa intambo apho esiludumbo 12 iye zibambene nayo. Kulo mzekelo, amathuba ngolwakhiwo unxantathu ilungelo luyanda kwi 95%.

Iimpawu ze amanani yokulingana

• I angle etsolo kwi unxantathu ekunene kunye icala enkulu leyo ilingana izinto ezifanayo unxantathu yesibini, - umqondiso zingenakuphikwa yamanani yokulingana. Thathela ingqalelo isixa engile, kulula ukungqina ukuba engile yesibini etsolo nazo ngokulinganayo. Ngoko ke, oonxantathu ezifanayo kule inkalo yesibini.
• Phezu yesicelo iziqwenga bobabini benza nabo ukwenzela ukuba ehambelanayo, ziye zaba enye unxantathu isosceles. Ngokutsho kwipropati zamaqela, hayi kanye mandithi, lo hypotenuse ilingana, kwakunye engile kwi kwisiseko, ngoko ke la manani ziyafana.

Ngokutsho lokuqala kulula kakhulu ukungqina ukuba oonxantathu ngokwenene bayalingana, logama nje ayalingana omnye amanye amaqela amabini ezincinane (okt. E. Imilenze).

Oonxantathu twatse ngokusekelwe II, ogama eneneni ubuxoki lenxaki emlenzeni kunye engile yayiyazi.

Iimpawu unxantathu a esinekona sasekunene

Ubude, leyo bewuhlisele evela esinekona sasekunene, yahlula inani ibe ngamaqela amabini alinganayo.

Emacaleni unxantathu ekunene kwaye udibaniso wayo kalula ngolawulo: amanqaku angumndilili, nto leyo uphumle phezu hypotenuse lilingana isiqingatha. iimilo Square ifumaneka zombini ifomula nguHeron, yaye isiqinisekiso ukuba ilingana isiqingatha imveliso kwezinye macala mabini.

Mihlaba engile egqithe engile unxantathu 30 ^o, 45 ^o 60 ^o.

• Kwi-engile, ngokucacileyo ilingana no ^30, kufuneka kukhunjulwe ukuba lecala eliphikisayo iya kulingana 1/2 iqela ngobukhulu.
• Ukuba engela ⁴⁵ °, ngoko ke angle yesibini etsolo nalo ⁴⁵ °. Oku kubonisa ukuba unxantathu yi isosceles kunye neentungo zayo bayalingana.
• Yipropathi engile ⁶⁰ lilele yokuba i engile wesithathu-degree unalo umlinganiselo ^we-30.

Le ndawo ngokulula elalivunyiwe lelinye ifomula ezintathu:

1. ngokusebenzisa ukuphakama icala apho uwe;
2. ifomula nyoni kaThixo;
3. emacaleni kunye engile ephakathi kwabo.

Emacaleni unxantathu ekunene, okanye mandithi imilenze idibane eziphakamileyo ezimbini ezahlukeneyo. Ukuze ufumane wesithathu, kuyimfuneko ukuba siqwalasele unxantathu onesiphumo, kwalandela theorem kaPythagoras ukubala ubude efunekayo. Ukongeza kule formula kukho kwakhona kabini umlinganiselo ndawo kunye nobude hypotenuse. Ibinzana iqhelekileyo phakathi kwabafundi lowo wokuqala, ekubeni kufuna izibalo ezimbalwa.

Theorem isicelo unxantathu ekunene

ilungelo unxantathu geometry kubandakanya ukusetyenziswa theorems ezifana:

1. theorem kaPythagoras. kubume bayo usendleleni yokuba isikweri hypotenuse ilingana udibaniso lwezikweri elinye macala mabini. Geometry Euclidean, lo mlinganiselo i isitshixo. Sebenzisa indlela unakho, ukuba banikwa unxantathu, umzekelo, SNH. SN - le hypotenuse, kwaye oko kuyimfuneko ukufumana. Ke SN ² = H. ² + HS ^2.
2. Cosine theorem. Ishwankathela theorem kaPythagoras: g ² = f ² + s -2fs ² * cos engile therebetween. Umzekelo, anikwe unxantathu IGAM. DB eyaziwa umlenze kunye hypotenuse NGABA, kufuneka ufumane i OB. Emva koko ifomula kuthatha uhlobo: OB ^{2 2} = DB + NGABA ² -2DB * NGABA * cos engile D. Kukho iziphumo ezintathu: kwikona etsolo-angled lo nxantathu na, ukuba udibaniso lwezikweri wamacala amabini square thabatha ubude wesithathu, umphumo kufuneka libengaphantsi kunonothi. Engela - obtuse, kulo mzekelo, ukuba ibinzana mkhulu kuno-zero. Engela - line kwi zero.
3. theorem sine. Ibonisa ukuzalana amaqela iikona eziphikisanayo. Ngamanye amazwi, le umlinganiselo ubude macala malunga i sine ye engile. Xa unxantathu HFB, apho hypotenuse na HF, kuya kuba yinyaniso: HF / isono engile B = FB / isono engile H = HB / isono engile F.