Kodi kupeza kutalika kwa chinthu cha makona equilateral? Chilinganizo malo, katundu msinkhu ndi makona equilateral

Masamu - sikungokhudza nkhani sukulu imene mukufuna mphambu wangwiro. Ndi kudziwa kuti nthawi zambiri zofunika pa moyo. Mwachitsanzo, pamene nyumba ya denga mkulu m'pofunika kuwerengera makulidwe a mitengo ndi chiwerengero chawo. Ndi zovuta ngati inu mukudziwa momwe kupeza kutalika kwa chinthu cha makona equilateral. nyumba mapulani zochokera chidziwitso cha katundu wa kanjedza zojambula. Mitundu ya nyumba nthawi zambiri zowoneka amafanana iwo. Mapiramidi Igupto, phukusi la mkaka, zojambulajambula, nsalu kupenta kumpoto ndipo ngakhale mikate - ndi Triangles onse ozungulira munthu. Monga Plato anati, dziko lonse zachokera Triangles.

isosceles makona

Kuti izo bwino, ngati ayankhidwa pansipa, tiyenera pang'ono kukumbukira ndizosowa Masamu.

The makona ndi isosceles ngati ali awiri mbali ofanana. Iwo nthawizonse kuitana mbali. Party amene miyeso amasiyana, wotchedwa zapansi.

mfundo zofunika

Ngati sayansi aliyense, Masamu amakhazikitsa malamulo omwe zikuluzikulu ndi mfundo. Ambiri a iwo. Taganizirani okhawo amene popanda mutu wathu adzakhala penapake bwinobwino.

Msinkhu - izi ndi mzere wolunjika kukopedwa perpendicular kwa mbali ina.

Apakatikati - mbali lotsogozedwa ndi aliyense vertex wa makona yekha pakati pa mbali ina.

Bisector - mtanda kuti ukugawa mu theka mbali.

Bisector wa makona ndi - ndi mwachindunji kapena kani, gawo bisector, kulumikiza pamwamba pa mbali ina.

Nkofunika kukumbukira kuti bisector kupendekeka kwa - ndi lamulo ray ndi makona bisector - gawo la mtengo wa.

The kumathandiza kupeza ngodya zabwino m'munsi mwa

The Lingaliro Lovomerezeka limanena kuti ngodya zili m'tsinde mwa makona aliyense isosceles nthawi zonse wofanana. Pofuna kutsimikizira Lingaliro Lovomerezeka imeneyi ndi lophweka. Ganizirani chochita isosceles makona ABC, imene AB = BC. Ku ABC bisector ngodya zofunika HP. Tsopano awiri chifukwa makona tiyenera kuziganizira. Pa chikhalidwe AB = BC, mbali HP wa Triangles ambiri, ndi kumathandiza kupeza ngodya zabwino AED ndi SVD ofanana, chifukwa VD - bisector. Kukumbukira chizindikiro choyamba cha kufanana, tikhoza kunena motsimikiza kuti Triangles ndi amaonedwa ofanana. Choncho, angelo onse okhudzidwa ndi ofanana. Ndipo, ndithudi, maphwando, koma ndi nthawi kuti nthawi ina.

Kutalika kwa makona isosceles

The Lingaliro Lovomerezeka lofunika, ozikidwa njira pafupifupi zonyozeka, ndi: kutalika mwa chinthu cha makona equilateral ndi bisector ndi apakatikati. Kuti timvetse tanthauzo lake othandiza (kapena akamanena) ayenera kuthandizidwa gawo. Kuti tichite zimenezi, kudula pepala isosceles makona. Chophweka njira kuchita izi kwa pepala wamba a kope mu bokosi.

Pindani makona chifukwa mu theka, aligning mbali. Kodi chinachitika? Awiri ofanana Triangles. Tsopano onani zopeka. Kukuza origami chifukwa. Lembani mzere khola. Ndi protractor onani mbali pakati pa mzere incised ndi kansalu m'munsi. Kodi mopendekeka ndi madigiri 90? chakuti mzere kukopedwa - perpendicular. Ndi tanthauzo - kutalika. Kodi kupeza kutalika kwa chinthu cha makona equilateral, ife kumvetsa. Tsopano ngodya pamwamba. Ntchito chimodzimodzi cheke protractor kumathandiza kupeza ngodya zabwino, tsopano anapanga kale mkulu. Ndi ofanana. Izi zikutanthauza kuti msinkhu ndi onse bisector. Titalandira mtsogoleri, kuyeza zigawo limene kutalika maziko a. Ndi ofanana. Choncho, kutalika mu makona equilateral bisects m'munsi ndipo ndi apakatikati.

chitsimikizo

Zooneka bwino ikusonyeza wa Lingaliro Lovomerezeka ndi. Koma Masamu - sayansi zolondola mokwanira, kotero n'zodziŵika.

Pa kulingalira Kuyanjana pakathi pa kumathandiza kupeza ngodya zabwino pa tsinde la anali atatsimikizira Triangles ofanana. Kumbukirani Wa - bisector, ndi Triangles AED ndi SVD ofanana. Poti anali kuti mbali lolingana wa makona ndi, ndithudi, angelo ali ofanana. Choncho AD = Sd. Choncho, Wa - apakatikati. Mpaka kutsimikizira kuti HP ndi mkulu. Potengera Kuyanjana pakathi pa Triangles kuganiziridwa likukhalira kuti makona wofanana mbali ADV kuwonjezera. Koma kumathandiza kupeza ngodya zabwino awiriwa moyandikana ndi akhala kuwonjezera mpaka madigiri 180. Choncho, chimene iwo ali? Kumene, 90 madigiri. Choncho, HP - ndi kutalika mu makona equilateral kukopedwa maziko a. QED.

mbali Ofunika

• Kukumana ndi mavuto, tiyenera kukumbukira mbali yaikulu ya isosceles Triangles. Amaoneka kuti ndi osiyanitsidwa Lingaliro Lovomerezeka.
• Ngati njira yothetsera vutolo wapezeka ndi Kuyanjana pakathi pa kumathandiza kupeza ngodya ziwiri, zikutanthauza kuti mukulimbana ndi makona isosceles.
• Ngati simungathe kutsimikizira kuti apakatikati ndi kutalika kwa makona ya, bwinobwino enclose - ndi makona atatu ndi isosceles.
• Ngati bisector ndi kutalika, ndiye, zochokera mbali yaikulu ya makona anatchula chinthu cha makona isosceles.
• Ndipo, ndithudi, ngati apakatikati ndi akutumikira monga msinkhu, monga kansalu - isosceles.

kutalika kwa chilinganizo 1

Komabe, ntchito kwambiri, muyenera kupeza masamu kutalika phindu. Ndicho chifukwa chake ife mmene kupeza kutalika kwa chinthu cha makona equilateral.

Tikaonanso chithunzi pamwambapa, ABC, imene - mbali - m'munsi. HP - kutalika kwa makona, iyenera chizindikiro h.

ndi makona AED chiyani? Popeza HP - kutalika, ndiye makona AED - amakona anayi mwendo kuti mukufuna kupeza. Kugwiritsa chilinganizo Pythagorean, ife kupeza:

= + AV² AD² VD²

Kumasulira VD akuti ndi m'malo mayina anatengera kale, ife kupeza:

N² = a² - (a / 2) ².

Uzichotsa muzu:

H = √a² - v² / 4.

Ngati inu kupanga ¼ chizindikiro cha muzu, ndiye njira zingakhale:

H = ½ √4a² - v².

Choncho ndi msinkhu ndi makona equilateral. Chilinganizo lachokera ku Lingaliro Lovomerezeka Pythagorean. Ngakhale ngati ife kuiwala kalembedwe chophiphiritsa, ndiye, podziwa njira za kafukufukuyu, inu nthawi zonse kubweretsa izo.

kutalika kwa chilinganizo 2

Chilinganizo tafotokozazi ndi zikuluzikulu ndi zambiri ntchito mu mavuto ambiri geometrical. Koma iye anali yekha. Nthawi zina anapereka m'malo mwa mtengo m'munsi anapatsidwa njingayo. Pamene deta monga kupeza kutalika kwa chinthu cha makona equilateral? Kuti athetse mavuto amenewa m'pofunika kugwiritsa ntchito chilinganizo osiyana:

H = ndi / tchimo α,

kumene H - kutalika, kwa maziko a,

ndi - mbali lateral,

α - ngodya pa maziko a.

Ngati vutoli wapatsidwa mbali pa vertex, ndi kutalika mwa chinthu cha makona equilateral chiri motere:

H = ndi / Ko (β / 2),

kumene H - kutalika, polowetsedwa maziko a ,,

β - mbali pa pamwamba pa,

ndi - mbali.

Kumanja isosceles makona

chidwi kwambiri katundu ali kansalu, pachimake pa umene uli wofanana ndi madigiri 90. Taonani bwino-angled makona ABC. Monga milandu yapita, Wa - kutalika kwa m'munsi lapansi.

The kumathandiza kupeza ngodya zabwino m'munsi ofanana. Kuwerengetsa ntchito yawo yaikulu sikungathetseretu:

α = (180 - 90) / 2.

Choncho, ngodya yomwe ili m'munsi, nthaŵi zonse pa madigiri 45. Tsopano tiyeni tione ADV makona. Iye ndi anayi. Ife tikupeza mbali AED. Ndi kuwerengetsera yosavuta ife kupeza madigiri 45. Ndipo, chotero, makona izi siziri zolondola kokha, komanso ndi isosceles. Mbali AD ndi VD ndi mumbali ndi ofanana.

Koma mbali AD nthawi yomweyo ndi theka Au. Iwo likukhalira kuti kutalika kwa chinthu cha makona equilateral ndi wofanana ndi theka m'munsi, ngati olembedwa mu mawonekedwe a chilinganizo ndi timapeza mawu otsatirawa:

H = ndi / 2.

Iwo siyenera kuti chilinganizo ichi ndi nkhani yapadera, ndipo angagwiritsidwe ntchito kokha kwa amakona anayi Triangles isosceles.

The Golden makona

chidwi kwambiri ndi makona golide. Mu chithunzi ichi, chiŵerengero mbali ya m'munsi ndi ofanana ndi maonekedwe ake, otchedwa chiwerengero cha Phidias. Pakona ili pamwamba - madigiri 36, ndi patsinde - madigiri 72. makona Izi anamusilira Pythagoreans. Golden Triangle mfundo kupanga maziko a kuchuluka kwa katswiri wosafa. Odziwika zisanu zisonga nyenyezi anamanga pa mphambano ya Triangles isosceles. Ntchito zambiri Leonardo da Vinci ntchito mfundo za "Golden Triangle". Zikuchokera "Mona Lisa" zachokera basi kanjedza, amene analenga pentagram bwino.

Penti "Cubism", mmodzi wa Pablo Pikasso ntchito, chidwi view ndipamene maziko a chinthu cha makona isosceles.