Chizindikiro choyamba cha kuyanjana kwa Triangles. Wachiwiri ndi wachitatu zizindikiro za kufanana kwa Triangles

Pakati pa nambala yaikulu polygons, amene ali kwenikweni sanali intersecting anatseka polygonal mzere, kansalu - ndi chithunzi ndi chiwerengero ang'onong'ono kumathandiza kupeza ngodya zabwino. M'mawu ena, ndi polygon yosavuta. Koma ngakhale kuphweka ake, chithunzi ichi Wobisa zambiri zinsinsi ndi chidwi limene limafotokoza nthambi wapadera wa masamu - Masamu. chilango m'masukulu kuyamba kuphunzitsa kalasi chiwiri, ndipo "Triangle" Mutu ndi mwapadera. Ana osati kuphunzira malamulo a chithunzi wokha, komanso kuyerekezera awo kuphunzira 1, 2 ndi 3, chizindikiro cha kuyanjana kwa Triangles.

Kudziwana loyamba

Mmodzi mwa malamulo woyamba, ndi bwino ophunzira, icho chimapita motere: Uwerenge kumathandiza kupeza ngodya zabwino za makona ndi wofanana madigiri 180. Kutsimikiza izi, suffices ntchito protractor kuyeza aliyense mfundo ndi kuwonjezera mfundo zonse chifukwa. Motero, mfundo ziwiri kudziwika mosavuta kudziwa lachitatu. Mwachitsanzo: Mu ngodya imodzi ya makona ndi 70 °, ndipo linalo - 85 °, zimene kukula kwa mbali yachitatu?

180 - 85 - 70 = 25.

Yankho: kuti ° 25.

Ntchito zingakhale zovuta, ngati chimodzi chokha yake phindu ngodya ndi phindu lachiwiri anati yekha mmene kapena kangati ndi wamkulu kuposa kapena zochepa.

Mu makona kudziwa ina mbali yache a mzere, omwe angathe kuchitidwa lili dzina lakelake:

• kutalika - mzere perpendicular limachokera ku vertex kuti mbali ina;
• misanje onse atatu, imachitika pa nthawi yomweyo, pakati pa zimakwana intersect, kupanga orthocenter, zomwe, malingana ndi mtundu wa makona kungakhale mkati ndi kunja;
• Apakatikati - mzere kulumikiza pamwamba pakati pa mbali ina;
• ndi mfundo ya mphambano ya medians wa ukulu wake, ndi mkati mawonekedwe ndi;
• bisector - mzere akuthamanga kuchokera pamwamba mpaka mphambano kutsidya linalo, mfundo ya mphambano ya bisectors atatu ndiko kuchimake kwa bwalo alembedwa.

Choonadi chosavuta za Triangles

Triangles, monga, ndithudi, ndi zithunzi zonse ndi makhalidwe awo ndi katundu. Monga tanenera kale, chithunzi ichi ndi polygon ophweka, koma ndi mbali yake khalidwe:

• motsutsa wautali kwambiri mbali ngodya zonse limakhala ndi chikuperekedwa zazikulu, ndi mosemphanitsa;
• ndi mbali ofanana ndi kumathandiza kupeza ngodya zabwino ofanana, chitsanzo - ndi isosceles makona atatu;
• Uwerenge kumathandiza kupeza ngodya zabwino mkati ndi nthawi wofanana 180 °, kuti kale anasonyeza chitsanzo;
• anakafika ku mbali imodzi ya makona ya aumbike kupitirira ngodya akunja omwe nthawizonse kukhala wolingana Uwerenge kumathandiza kupeza ngodya zabwino, izo ziribe pafupi;
• aliyense wa zipani nthawi zonse pasanathe Uwerenge mbali zina ziwiri, koma ambiri kusiyana.

mitundu ya Triangles

Kuyang'ana siteji yotsatira ndi kupeza gulu limene anapereka makona. Kukhala mtundu makamaka zimadalira mfundo za kumathandiza kupeza ngodya zabwino za makona a.

• Isosceles - ndi magulu awiri ofanana otchedwa mbali, wachitatu mu nkhani iyi amachita monga akalumikidzidwa m'munsi. The kumathandiza kupeza ngodya zabwino patsinde pa makona ndi chimodzimodzi ndi apakatikati kukopedwa kuchokera pamwamba, ndi bisector ndi kutalika.
• Zolondola, kapena kansalu equilateral - ndi imodzi imene m'mbali mwake onse ndi ofanana.
• Amakona anayi imodzi m'makona ake ndi 90 °. Pankhaniyi, mbali ina ngodya uwu umatchedwa hypotenuse, ndi ena awiri - miyendo.
• Pachimake makona - pa kumathandiza kupeza ngodya zabwino zosakwana 90 °.
• Obtuse - mmodzi wa kumathandiza kupeza ngodya zabwino woposa 90 °.

Kulingana ndi kufanana kwa Triangles

Mu ndondomeko ya maphunziro sikuti maganizo payokha anatengedwa mawonekedwe, komanso kuyerekeza Triangles awiri. Ndipo ichi mutu yooneka ngati yosavuta ali zambiri malamulo ndi theorems sipangakhalenso anasonyeza kuti chiwerengero ankaona - Triangles ofanana. Zizindikiro za Triangles ali ndi tanthauzo la chilingano: ndi Triangles ofanana ngati mbali lolingana ndi kumathandiza kupeza ngodya zabwino ndi ofanana. Ndi aone kuti pali uwu, ngati ife amalowerera Chiwerengerochi awiri pa wina ndi mzake, mizere awo onse converge. Komanso chithunzi zikhoza kukhala zofanana, makamaka, izo nkhawa zayamba akalumikidzidwa zofanana, anasiyana kokha ukulu. Pofuna kupanga maganizo amenewo pa Triangles akuimira ayenera kukwaniritsa chimodzi cha zinthu zotsatirazi:

• kumathandiza kupeza ngodya ziwiri chithunzi chimodzi ndi wofanana kumathandiza kupeza ngodya ziwiri wina;
• molingana ndi mbali ziwiri mbali ziwiri za makona wachiwiri, ndi kumathandiza kupeza ngodya zabwino za mbali anapanga ndi zofanana;
• mbali zitatu za chithunzi chachiwiri ndi mofanana woyamba.

N'zoona kuti Kuyanjana pakathi yamphamvu, amene sayambitsa kukaikira pang'ono, muyenera kukhala ndi makhalidwe a mbali zonse za kanjedza onse, koma ndi vuto la chiphunzitso ndi wosalira kwambiri, ndipo chabe zinthu zochepa kuloledwa kutsimikizira kuti Triangles lapansi.

Chizindikiro choyamba cha kuyanjana kwa Triangles

pa mutu wa mavuto ndi kuthetsedwa pamaziko a umboni wa Lingaliro Lovomerezeka, amene awerenga motere: ". Ngati mbali ziwiri za makona komanso mbali yomwe iwo amapanga, ndi ofanana ndi mbali ziwiri ndi mbali ya makona ena, ndiye manambalawo komanso ofanana ndi mnzake"

Monga umboni mawu a Lingaliro Lovomerezeka za chizindikiro cha kuyanjana kwa Triangles? Aliyense akudziwa kuti zigawo ziwiri ofanana ngati iwo ali ndi kutalika, kapena circumference ofanana ngati iwo ali ndi utali wozungulira chomwecho. Ndipo pa nkhani ya makona ya pali zizindikiro zochepa zimene zikhoza kapadera kuti manambalawo zofanana, zomwe ndi zothandiza kuthetsa mavuto osiyanasiyana zojambula.

Kulira kwa Lingaliro Lovomerezeka "The chizindikiro choyamba cha kuyanjana kwa Triangles", tafotokozazi, koma umboni wake:

• Tiyerekeze makona ABC ndi ₁ B ₁ C ₁ ndi mbali yomweyo AB ndi ₁ B ₁ ndipo motero, BC ndi B ₁ C _1, ndi kumathandiza kupeza ngodya zabwino zimene anapanga ndi mbali awa ndi phindu chomwecho, i.e. ofanana. Kenako pa ABC △ △ A ₁ B ₁ C _1, ife tikufika machesi mizere onse ndi mfundo. Tidziwanso kuti Triangles awa ali chimodzimodzi, kutanthauza ofanana.

Lingaliro Lovomerezeka "The chizindikiro choyamba cha kuyanjana kwa Triangles," umatchedwanso "Pa mbali ziwiri ndi ngodya." Kwenikweni, zimenezi ndicho icho.

Lingaliro Lovomerezeka pa chizindikiro yachiwiri

The chizindikiro chachiwiri ofanana imatsimikizirika chimodzimodzi, umboni zachokera chakuti imposition wa ndalama pa wina ndi mzake, iwo zofanana mu nsonga zonse ndi mbali. Lingaliro Lovomerezeka A zikumveka ngati izi: "Ngati mbali imodzi ndipo kumathandiza kupeza ngodya ziwiri mu mapangidwe umene nawo, ndi Party ndi ngodya ziwiri za makona chachiwiri, ndiye Chiwerengerochi zofanana, mwachitsanzo ofanana."

The chizindikiro chachitatu ndi umboni

Ngati onse 2 ndi 1 chizindikiro ofanana imakhudzanso mbali zonse za Triangles, angelo ndi mosiyanasiyana, wachitatu likukamba chabe kwa magulu. Choncho, Lingaliro Lovomerezeka ali ndi mawu awa: "Ngati mbali zonse za makona ali wofanana mbali zitatu za makona chachiwiri, manambalawo zofanana."

Pofuna kutsimikizira Lingaliro Lovomerezeka izi, m'pofunika wofufuza mwatsatanetsatane tanthauzo la ofanana. Ndipotu tanthauzo la "Triangles ofanana"? Umunthu limanena kuti ngati ife amalowerera chithunzi wina ndi mzake, onse mbali agwirizane, likhoza kukhala choncho pamene nthiti Zawo ndi kumathandiza kupeza ngodya zabwino ndi ofanana. Pa nthawi yomweyo mbali zosiyana mbali imodzi, amene ali ofanana ndi makona atatu ena ndi wofanana ndi vertex lolingana wa chithunzi chachiwiri. Tikumbukenso kuti pa nthawiyi umboni n'zosavuta lakuti 1 chizindikiro cha kuyanjana kwa Triangles. Ngati ndondomeko izi anati, Kuyanjana pakathi pa Triangles sangathe, koma pa nthawi imene chithunzi ndi galasi chifanizo cha woyamba.

Triangles bwino

Kapangidwe ka Triangles ngati nthawizonse vertex ndi 90 ° ngodya. Choncho, mfundo zotsatirazi zomwe ziri zowona:

• Triangles ndi mlingo woyenerera ofanana ngati miyendo ya cathetus chachiwiri zofanana;
• kanjedza ndi ofanana ngati iwo ali wofanana ndi hypotenuse ndi mmodzi wa miyendo;
• Triangles amenewa ndi ofanana ngati miyendo yawo zofanana pachimake oyenerera.

Mbali zikugwirizanirana Triangles anayi. Pofuna kutsimikizira Lingaliro Lovomerezeka ntchito mosiyanasiyana app wina ndi mzake, chifukwa mu miyendo ya Triangles ndi apangidwe kuti awiri molunjika kumanzere molunjika ngodya ndi CA ₁ ndi CA mbali.

Mavalidwewa

Nthawi zambiri, mu kuchita, kugwiritsidwa ntchito chizindikiro cha kuyanjana kwa Triangles. Ndipotu, izi kalasi yooneka ngati yosavuta kwa Masamu ndi ndege Masamu ntchito mfundo ndi 7 kuwerengera kutalika Mwachitsanzo, foni chingwe popanda m'dera muyeso, chimene chidzachitika. Kugwiritsa Lingaliro Lovomerezeka izi n'zosavuta kuti kuwerengetsera zofunika kudziwa kutalika wa chisumbucho, m'katikati mwa mtsinje, popanda kusambira kudutsa izo. Kapena kuwonjezera mpanda poika bala mu Bay moti lagawidwa Triangles awiri ofanana, kapena kuwerengera zinthu zovuta ntchito matabwa kapena mu mawerengedwe a dongosolo truss denga pa ntchito yomanga.

Chizindikiro choyamba cha kuyanjana kwa Triangles ali ntchito lonse mu weniweni "wamkulu" moyo. Ngakhale mu zaka sekondale ndi mutu ochuluka zikuwoneka wotopetsa ndi zosafunika kwathunthu.