Kodi kupeza mbali ya kansalu bwino? Ndizosowa Masamu

Miyendo ndi hypotenuse - mbali ya kansalu bwino. Choyamba - ichi ndi zigawo amene ali pafupi ndi mlingo woyenerera ndi hypotenuse ndi gawo wautali kuposa chithunzi ndi popenyana ndi ngodya ^90. Pythagorean makona amatchedwa mbali imodzi ndiwo manambala achilengedwe kutalika Pankhaniyi amatchedwa "Pythagorean umaŵirikiza nthaŵi zitatu".

makona Igupto

Kuti mbadwo pano waphunzira Masamu mu mawonekedwe chimene chimaphunzitsidwa sukulu tsopano, izo zachitika zaka zingapo. Amaona yofunika kwambiri kuti Lingaliro Lovomerezeka Pythagorean. mbali amakona anayi a pa makona (zimakwana amadziwika kuti dziko lonse lapansi) ndi 3, 4, 5.

Ochepa amene sali bwino mawu oti "mathalauza Pythagorean malangizo onse ndi ofanana." Koma kwenikweni, Lingaliro Lovomerezeka zikumveka kukhala: c ² (lalikulu la hypotenuse a) = ² + b ² (Uwerenge mabwalo miyendo).

Mwa masamu makona ndi mbali 3, 4, 5 (onani, mamita ndi r Mukhoza. D.) Kodi "Iguputo. N'zochititsa chidwi kuti utali wozungulira bwalo kuti linalembedwa mu chithunzi wofanana wina. dzina kunayamba m'zaka za m'ma V BC, pamene Agiriki anapita ku Iguputo.

Pamene akumanga piramidi mapulani ndi oyeza ntchito chiŵerengero 3: 4: 5. Nyumba kulandira m'thumba, zabwino kwambiri ndi lalikulu, ndipo kawirikawiri anakomoka.

Kumanga njira yoyenera, omanga ntchito chingwe limene mfundo 12 wakhala ananamizira. Pankhaniyi, Mwina kumanga kansalu lamanja ziwonjezeke kwa 95%.

Zizindikiro za kanjedza kufanana

• Ngodya pachimake mu kansalu bwino ndi mbali yaikulu yomwe ndi wofanana ndi zinthu zomwezo mu makona chachiwiri, - ndi osatsutsika chizindikiro cha kanjedza ofanana. Mogwirizana ndi kuchuluka kwa kumathandiza kupeza ngodya zabwino, n'zosavuta kutsimikizira kuti chachiwiri kumathandiza kupeza ngodya zabwino pachimake komanso ali ofanana. Choncho, Triangles ali chimodzimodzi chinthu chachiwiri.
• Pa ntchito zidutswa ziwiri pa wina ndi mzake atembenuza moti zimayenderana, akhala limodzi isosceles makona. Malinga ndi chuma cha zipani, kapena kani, hypotenuse ndi ofanana, komanso kumathandiza kupeza ngodya zabwino pa maziko, ndipo kotero Chiwerengerochi ali ofanana.

Malinga ndi mbali yoyamba n'zosavuta kwambiri kuti atsimikizire kuti Triangles ndithu ofanana, malingana ngati awiri maphwando ang'onoang'ono (ie. E. miyendo) ndi ofanana ndi mnzake.

Triangles zofanana pamaziko a II, amene zomwenso lagona aone kuti pali mwendo ndi makona pachimake.

Katundu wa makona ndi njira yoyenera

Msinkhu, amene anali adatchithisira ku mlingo woyenerera, ukugawa chithunzi m'magulu awiri ofanana.

m'mbali mwa kansalu chabwino ndi apakatikati ake mosavuta anazindikira mwa ulamuliro: ndi apakatikati, amene akupuma pa hypotenuse ndi wofanana ndi theka la izo. akalumikidzidwa Square angapezeke onse pa njira chimeza, ndi kutsimikizira kuti ndi wofanana ndi mankhwala theka la mbali zina ziwiri.

katundu ndi angled makona kumathandiza kupeza ngodya 30 ^O, 45 ^Inu ndi 60 ^Inu.

• Pa ngodya, chimene ndi wofanana ndi ^zaka 30, tiyenera kukumbukira kuti wakutsutsana adzakhala wofanana 1/2 chipani waukulu.
• Ngati mbali ndi ⁴⁵ °, kotero wachiwiri pachimake ngodya ndi ⁴⁵ °. Zimenezi zikusonyeza kuti makona ndi isosceles ndi miyendo yake ndi ofanana.
• Chuma cha ngodya ⁶⁰ kwagona kuti lachitatu degree ali ndi muyeso ^wa 30.

dera mosavuta anazindikira ndi mmodzi mwa mitunduyi zitatu:

1. kudzera kutalika ndi mbali imene imagwera;
2. chilinganizo chimeza ndi;
3. mbali ndi mbali pakati pawo.

m'mbali mwa kansalu lamanja, kapena m'malo miyendo converge Kumwamba awiri osiyana. Kupeza wachitatu, m'pofunika kuganizira makona chifukwa, kenako ndi Lingaliro Lovomerezeka Pythagorean kuwerengetsa zaka chofunika. Kuwonjezera pa njira imeneyi palinso kawiri m'dera chiŵerengero ndi kutalika kwa hypotenuse lapansi. Mawu ambiri mwa ophunzira ndi kuyamba pamafunika kuwerengetsera ochepa.

Lingaliro Lovomerezeka ntchito kwa makona bwino

chabwino makona Masamu zikuphatikizapo ntchito theorems monga:

1. Pythagorean Lingaliro Lovomerezeka. Kwenikweni ake kwagona kuti m'bwalo la hypotenuse ndi wofanana Uwerenge mabwalo mbali zina ziwiri. Mu Masamu Euclidean, chiŵerengero iyi ili fungulo. Ntchito chilinganizo mwina, ngati kupatsidwa makona Mwachitsanzo, SNH. SN - ndi hypotenuse, ndipo m'pofunika kupeza. Ndiye SN ² = NH ² + HS ^2.
2. Cosine Lingaliro Lovomerezeka. Mwachidule Lingaliro Lovomerezeka Pythagorean: ga ² = f ² + m ² -2fs * Ko ngodya therebetween. Mwachitsanzo, anapatsidwa kansalu DOB. DB kudziwika mwendo ndipo hypotenuse KUCHITA, muyenera kupeza ob. Ndiye chilinganizo amatenga mawonekedwe: ob ^{2 2} = DB + KODI ² -2DB * KODI * Ko ngodya D. Pali zotsatira atatu: pachimake-angled ngodya ya makona ndi, ngati Uwerenge mabwalo mbali ziwiri za lalikulu kuchotsera kutalika lachitatu, chifukwa ayenera kukhala osachepera ziro. Ngodya - obtuse, mu Zikatero, ngati mawu ali wamkulu kuposa ziro. Ngodya - mzere pa ziro.
3. Sine Lingaliro Lovomerezeka. Izo zimasonyeza ubale wa zipani ku ngodya otsutsanawa. M'mawu ena, chiŵerengero cha kutalika kwa mbali zosiyana kwa sine wa kumathandiza kupeza ngodya zabwino. Mu makona HFB, mmene hypotenuse ndi HF, zidzakhala zoona: HF / tchimo ngodya B = FB / tchimo ngodya H = HB / tchimo ngodya F.