Yadda za a sami tsawo daga wani equilateral alwatika? Formula wuri, tsawo Properties a wani equilateral alwatika

Lissafi - yana da ba kawai a makaranta magana a kan abin da za ka bukatar ka sami cikakken ci. Shi ne kuma wani ilmi game da cewa sau da yawa ake bukata a rayuwa. Alal misali, a lõkacin da gina wani gidan da wani babban rufin wajibi ne yin lissafi da kauri daga cikin rajistan ayyukan da kuma lambar. Yana da sauki idan ka san yadda za ka sami tsawo daga wani equilateral alwatika. Gine-gine ginen da su ne bisa ilimi da kaddarorin lissafi Figures. A siffofin gine-gine sukan gani kama su. A kasar Masar pyramids, da kunshe-kunshe da madara, m raƙĩƙi, da arewacin zanen da ko da wuri - duk triangles kewaye mutumin. Kamar yadda Plato ce, dukan duniya ta dogara ne a kan triangles.

isosceles alwatika

Don yin shi bayarda, kamar yadda za a tattauna a kasa, yana da daraja a bit a tuna da kayan yau da kullum na lissafi.

A alwatika ne isosceles idan yana da biyu daidaita bangarorin biyu. Su ko da yaushe kira gefe. Jam'iyyar wanda girma ya bambanta, ya kira sansanonin.

asali Concepts

Kamar kowane kimiyya, lissafi na da asali dokoki da kuma kyama. A yawa daga gare su. La'akari kawai waɗanda bã su da wanda mu theme zai zama da ɗan m.

Height - wannan shi ne tafarki line kõma perpendicular zuwa kishiyar sashi.

Tsakãtsaki ce - a kashi directed daga kowane kokuwa na alwatika kawai zuwa tsakiyar gefen.

Bisector - wani katako da ya rabu a rabin da kwana.

Bisector na alwatika - shi ne mai kai tsaye, ko kuma wajen, da kashi bisector, a haɗa da saman kishiyar sashi.

Yana da muhimmanci a tuna cewa bisector na kwana - shi ne wajibi ray da alwatika bisector - wani ɓangare na katako.

A tushe kusassari na

A Theorem jihohin da sasanninta suna located a tushe na wani isosceles alwatika ne ko da yaushe daidaita. Don tabbatar da wannan Theorem ne mai sauqi qwarai. La'akari da nuna wani isosceles alwatika ABC, a cikin abin da AB = BC. Daga ABC bisector kwana zama dole to HP. Yanzu biyu sakamakon alwatika kamata a yi la'akari. A cikin yanayin AB = BC, da HP gefe na triangles a general, da malã'iku AED da SvD ne daidai, saboda VD - bisector. Ambatar farko alamar daidaitaka, za mu iya lafiya kammala da cewa, triangles suna dauke daidai. Saboda haka, duk dacewa kusassari ne daidai. Kuma, ba shakka, da jam'iyyun, amma da cewa lokaci zai koma baya.

A tsawo daga cikin isosceles alwatika

Da muhimman hakkokin Theorem, wanda dogara ne mafita ga kusan dukkan ayyuka, shi ne: tsawo a cikin wani equilateral alwatika ne bisector da tsakãtsaki ce. Don fahimta ta m ji (ko jigon) ya sanya goyon bayan izni. Don yin wannan, yanke takarda isosceles alwatika. A mafi sauki hanyar yin wannan daga talakawa takardar da rubutu a cikin akwatin.

Ninka da sakamakon alwatika a rabin, aligning bangarorin. Abin da ya faru? Biyu daidai triangles. Yanzu duba ƙiri. Expand sakamakon Origami. Zana a ninka line. Tare da protractor duba kwana tsakanin incised line kuma a alwatika tushe. Menene kwana na 90 digiri? Gaskiyar cewa line kõma - perpendicular. By definition - tsawo. Yadda za a sami tsawo daga wani equilateral alwatika, mun gane. Yanzu ga sasanninta a saman. Amfani da wannan rajistan shiga protractor malã'iku, yanzu kafa riga high. Su ne daidai. Wannan yana nufin cewa da tsawo ne duka bisector. Amfani da makamai da wani mai mulki, auna segments a cikin abin da tsawo daga tushe. Su ne daidai. Saboda haka, da tsawo a wani equilateral alwatika bisects tushe da kuma shi ne mai tsakãtsaki ce.

A hujja

Kayayyakin AIDS a fili da inganci na Theorem. Amma lissafi - da kimiyya m isa, don haka ne bayyanannu.

A lokacin da la'akari da daidaici da kusassari a gindi ya tabbatar daidai triangles. Ka tuna, WA - bisector, da kuma triangles AED da SvD ne daidai. A ƙarshe ya cewa m bangarorin na alwatika kuma, ba shakka, da malã'iku ne daidai. Saboda haka AD = SD. Sanadiyar haka, WA - tsakãtsaki ce. Ya zauna ya tabbatar da cewa HP ne high. Bisa ga daidaici da triangles shawara, shi dai itace cewa wani kwana daidai da kwana Adv ƙara. Amma wadannan biyu kusassari ne m, kuma da aka sani ya ƙara har zuwa 180 digiri. Saboda haka, abin da suka kasance? Hakika, 90 digiri. Saboda haka, HP - shi ne tsawo a wani equilateral alwatika kõma zuwa ga tushe. QED.

key siffofin

• Don hadu da kalubale, ya kamata ka tuna da babban fasali na isosceles triangles. Suka ze zama kishiya Theorem.
• Idan a cikin shakka daga warware matsalar gano da daidaici da biyu kusassari, yana nufin cewa kana tare ne da wani isosceles alwatika.
• Idan ba ka iya tabbatar da cewa tsakãtsaki ce shi ne ma da tsawo daga cikin alwatika, a amince ƙulla - da alwatika ne isosceles.
• Idan bisector ne tsawo, sa'an nan, dangane da babban fasali na alwatika ake magana a wani isosceles alwatika.
• Kuma, ba shakka, idan tsakãtsaki ce da hidima a matsayin tsawo, irin wannan alwatika - isosceles.

da tsawo daga cikin Formula 1

Duk da haka, domin mafi ayyuka, kana bukatar ka sami ilmin lissafi tsawo darajar. Wannan shi ne dalilin da ya sa muka yi la'akari da yadda za a sami tsawo daga wani equilateral alwatika.

Komowa zuwa sama adadi, ABC, wanda mai - daban a - tushe. HP - tsawo daga cikin alwatika, shi yana cikin h alama.

Mene ne alwatika AED? Tun HP - tsawo, sa'an nan da alwatika AED - rectangular kafar cewa kana so ka sami. Amfani da Pythagorean dabara, muna samun:

= + AV² AD² VD²

Ma'ana da magana VD da kuma musanya zane-zane da soma a baya, mun samu:

N² = a² - (a / 2) ².

Dole ne ka cire tushen:

H = √a² - v² / 4.

Idan ka yi ¼ na ãyã daga cikin tushen, sa'an nan da dabara zai zama:

H = ½ √4a² - v².

Saboda haka ne tsawo a wani equilateral alwatika. Da dabara samu daga Pythagorean Theorem. Ko da idan muka manta da m tsarin rubutu, sa'an nan, da sanin da hanyar da binciken, za ka iya ko da yaushe kawo shi.

da tsawo daga cikin dabara 2

Da dabara aka bayyana a sama shine tushen da kuma fi amfani a mafi yawan geometrical matsaloli. Amma ta kasance ba kadai. Wani lokaci yana bayar maimakon wani tushe darajar ba kwana. Lokacin data kamar gano wani tsawo na wani equilateral alwatika? Don warware wadannan matsaloli shi ne bu mai kyau don amfani mai daban-daban dabara:

H = wani / zunubi α,

inda H - tsawo, zuwa ga tushe,

da kuma - a kaikaice gefen,

α - kwana a tushe.

Idan matsalar da aka bai wa kwana a kokuwa, da tsawo a cikin wani equilateral alwatika ne kamar haka:

H = wani / cos (β / 2),

inda H - tsawo, saukar da tushe ,,

β - da kwana a koli,

da kuma - bangarorin.

Dama isosceles alwatika

Da ban sha'awa sosai dukiya yana da wani alwatika, koli na wanda yake daidai da 90 digiri. La'akari da wata dama-angled alwatika ABC. Kamar yadda a baya lokuta, WA - tsawo wajen tushe.

A tushe kusassari ne daidai. Lissafta su manyan aikin ba zai yi:

α = (180 - 90) / 2.

Saboda haka, sasanninta located a tushe, ko da yaushe a 45 digiri. Yanzu la'akari Adv alwatika. Ya kuma shi ne rectangular. Mun sami kwana AED. By sauki lissafin da muka samu 45 digiri. Kuma, saboda haka, wannan alwatika ne ba kawai dama, amma kuma wani isosceles. A tarnaƙi AD kuma VD ne bangarorin da suke daidai.

Amma gefen AD a lokaci guda shi ne rabin da AU. Sai dai itace cewa a cikin tsawo na wani equilateral alwatika ne daidai da rabin da tushe, kamar yadda idan aka rubuta a cikin wani nau'i na dabara, mu sami wadannan magana:

H = wani / 2.

Ya kamata kada a manta da cewa wannan dabara ne kawai na musamman hali, kuma za a iya amfani kawai ga rectangular isosceles triangles.

The Golden alwatika

Very ban sha'awa shi ne da zinariya alwatika. A wannan adadi, da rabo daga cikin gefe na da tushe ne daidai da darajar, da ake kira yawan Phidias. Kusurwa located a saman - 36 digiri, tare da tushe - 72 digiri. Wannan alwatika ganin darajarsa Pythagoreans. Golden Bamuda ka'idojin samar da tushen wani jam'i na m Masterpieces. Sanannun biyar-nuna star gina a yankunan isosceles triangles. Domin da yawa ayyukan Leonardo Vinci amfani da manufa na "zinariya alwatika". Abun da ke ciki "Mona Lisa" dogara ne kawai a kan Figures, wanda ƙirƙirar dama pentagram.

Zanen "Cubism", daya daga Pablo Pikasso aiki, m view Forms da akai na wani isosceles alwatika.