Pehea e imi i ke kiekie o ka equilateral triangle? Haʻilula wahi, kiekie waiwai i loko o ka equilateral triangle

Anahonua - ka mea, aole pono i kekahi kula kumuhana ma a e pono e kiʻi i ka manual hemolele. Ua mea no hoi i ike i ua pinepine koi 'ia i loko o ke ola. No ka laʻana, ka wā kukulu ana i ka hale me ka hale kiʻekiʻe mea pono e hoʻomaulia i ka mānoanoa o ka pauku, a me ko lakou helu. ʻO oluolu ina e ike pehea e imi i ke kiekie o ka equilateral triangle. Kuhikuhipuʻuone hale i ka nānā 'ana ma luna o ka ike ana o ka waiwai o geometric huahelu. Ke ano o ka hale i pinepine visually e hoohalike ai ia. Ke kanaka o Aigupita pyramids, i nā pūʻolo helu o ka waiū, noʻeau humuhumu,'ākau pena, a hiki hūʻole - a pau na triangle mauna a puni i ke kanaka. Like Plato mai la, ke ao nei a pau ua me ka nānā 'ana ma triangle mauna.

isosceles triangle

E hana ia clearer, like e e kūkā mai ma lalo nei, e pono ke kuai i ka iki, e hoomanao i ka hoʻokumu paʻaʻana o ka anahonua.

Ke triangle Ua isosceles ina ia he mau likeʻaoʻaoʻelua. Lakou mau kapa akuʻaoʻao. Party kona Ana OAOOUIEeE, i kapaʻia ko lākou mau kumu.

walaʻauʻana manaÿo

Like kekahi 'epekema, anahonua i kona mau walaʻauʻana rula a me ka manaÿo. A hailona no ia. wale ka poe ole a mākou theme like e e kekahi unclear noonoo.

Kiekie - keia mea he pololei laina e holo ana ÷ haku i kaʻaoʻao e ku pono ana.

Median - he Hoʻohana kauoha mai kēlā me kēia vertex o ka triangle wale a hiki i ka waena o kaʻaoʻao e ku pono.

Bisector - he laau i hookaawale ai i ka hapalua o ka huina.

Bisector o ka triangle - ia mea ma ke ala, a, e, i ka Hoʻohana bisector, ai pili aku i ka luna o kaʻaoʻao e ku pono.

He nui no ka hoomanao ana i ka bisector o ka huina - ia mea obligatory Ray a me ka triangle bisector - i kekahi hapa o ka mea ulana lole.

Ke kumu pana pua o

Ke theorem Hawaii i na kihi i aia ma ke kumu o kekahi isosceles triangle i manawa like. E hoao i kēia theorem ka loa mea. Noonoo hōʻike he isosceles triangle ABC, ma a AB = BC. Mai ABC bisector ka makau pono ia HP. Ano, e e noʻonoʻo i ke kūpono triangle elua. Ma ke ano AB = BC, ka HPʻaoʻao o ka triangle mauna i ka nui, a me ka pana pua AED a me SVD i like, no ka mea, VD - bisector. Hoomanao ana i ka hoailona mua o ka like, ua hiki pakele manao nei makou, o ka triangle mauna i manaoia like. Nolaila, nā mea a pau pili pana pua i like. A, o ka papa, na aoao elua, aka, ma ia manawa, e hoʻi hope.

Ke kiekie o ka isosceles triangle

Ke kahua theorem, i ua ma muli pāʻoihana no kaʻaneʻane nā hana, o: kona kiʻekiʻe i loko o ka equilateral triangle o ka bisector a me Media. E maopopo kona mea hiki hoohalike ( 'ole o Mānoa,) e e kākoʻo wahiʻai. E hana i kēia,ʻoki pepa isosceles triangle. Ke easiest alanui, e hana i kēia, mai ka maʻamau pepa o ka puke noke i loko o ka pahu.

E pelu i ka kūpono triangle ma ka hapa, aligning na aoao elua. Ua aha 'ia? Elua like triangle mauna. Ano, e kaha i ka ke koho. E ho'ākea i ke kūpono origami. E kaha i ka pa laina. Me ka protractor e kaha i ka huina ma waena o ka incised laina, a me ka triangle kumu. He aha ke ano o ka huina o 90 degere? Ka nui, e hoike ana o ka laina e holo ana - ÷ haku. By ka wehewehena - kiʻekiʻe. Pehea e imi i ke kiekie o ka equilateral triangle, ua maopopo mākou. Ano, no na kihi i ka luna. E ho ohana i ka ia ponopono protractor pana pua, ua manawa i hanaʻia kiʻekiʻe kāinoa mua. Ka mea, e like. Kēia 'o ia hoʻi i ka mea kiʻekiʻe o nā bisector. Kahikoia me ka luna, e ana i ka Hoʻohana i loko i ke kiekie o ka waihona ipu. Ka mea, e like. Nolaila, ke kiekie ma ka equilateral triangle bisects ka waihona ipu a me ka mea i ka Media.

ke hooiaio

Pelaha maopopo hōʻike i ka ho'ōia o ka theorem. Akā, anahonua - ka 'epekema pololei lawa, no laila, hoʻoponopono-akaka no.

Ma noonoo no ka like ana o pana pua i ka waihona ipu, ua hoao like triangle mauna. Hoʻomanaʻo aʻela nō, WA - bisector, a me na triangle mauna AED a me SVD i like. Ka hopena ua i ka like aoao o ka triangle, a, o ka papa, i ka pana pua i like. No laila, AD = SD. Nolaila, WA - Media. Ua koe e hooiaio ia HP mea kiʻekiʻe. Ma muli o ka like o triangle mauna noonoo, e huli mai i ka huina like no ka huina ADV Kuʻina. Akā, i kēia mau pana pua mau mea e pili a me ka ua, ua ike e hoonui mai i ka 180. Nolaila, i ka mea e? O ka holo ana, 90 degere. Penei, HP - o ke kiekie ma ka equilateral triangle e holo pololei ana i ka waihona ipu. QED.

Key hiʻona

• E hālāwai me ka hana nui loa ia, ka mea, e hoomanao oukou i ka papa kuhikuhiE hiʻona o isosceles triangle mauna. Ka mea, he e ia i ka inverse theorem.
• Inā i loko o ka papa o ka hoʻoponopono i ka pilikia 'akomi i ma ka like o ka mau pana pua, ka mea,' o ia hoʻi ia oe e ana i ka isosceles triangle.
• Inā 'oe e hiki e hooiaio i ka Media mea i ke kiekie o ka triangle, pakele apo ai - ka triangle mea isosceles.
• Inā ka bisector o ke kiʻekiʻe, a laila, ma muli o ka nui hiʻona o ka triangle haawiia keia i ka isosceles triangle.
• A, o ka papa, ina ka Media a me ka lawelawe 'ana me ke kiekie, e like me ka triangle - isosceles.

i ke kiʻekiʻe o ka haʻilula 1

Eia naʻe, no ka hapanui mau hana, e pono e huli i ka makemakika kiʻekiʻe waiwai. Ia mea, ua hoomanao i ke ano, e imi i ke kiekie o ka equilateral triangle ke kumu.

A hoʻi hou aʻela ia i ka luna huahelu, ABC, ma a ka - aoao ma - kumu. HP - i ke kiekie o ka triangle, ka mea, i ka h palena hōʻailona.

He aha ka ke triangle AED? No ka HP - kiʻekiʻe, laila, i ka triangle AED - huinahń wāwae i kou makemake, e huli. E ho ohana i ka Pythagorean haʻilula, ua loaʻa:

= + AV² AD² VD²

Wā o ka hōʻike VD, a hookomoia designations hookama mua, ua loaʻa:

N² = a² - (he / 2) ².

Oe e wehe i ke kumu:

H = √a² - v² / 4.

Inā 'oe e ka ¼ o ka hoailona o ke kumu, a laila, i ka haʻilula makemake e:

H = ½ √4a² - v².

Pela o ke kiekie ma ka equilateral triangle. Ke haʻilula loko mai o ka Pythagorean theorem. Oia hoi, ina ua poina i ka symbolic notation, laila, e ike ana i ke ano o ka mea i hoʻoholo ', e hiki mau lawe mai ia.

i ke kiʻekiʻe o ka haʻilula 2

Ka haʻilula ho'ākāka 'ia ma luna o ka hoʻokumu a me ka hapanui mau hana i loko o ka hapanui o geometrical pilikia. Akā,ʻo ia ua i ka mea wale nō kekahi. I kekahi manawa ka mea, aka ma ka hakahaka o ka waihona ipu waiwai i haawiia mai huina. I kaʻikepili e like me ka loaa ole o ke kiekie o ka equilateral triangle? E hoʻoponopono i kēia mau pilikia ia mea kupono e hoʻohana i kaʻokoʻa haʻilula:

H = i / hewa α,

kahi H - kiʻekiʻe, ma ke kumu,

a - he kīloi paʻewaʻaoʻao,

α - huina i ke kumu.

Inā ua hāʻawi mai i ka pilikia o ka huina ma ka vertex, ke kiekie i loko o ka equilateral triangle mea like penei:

H = i / cos (β / 2),

kahi H - kiʻekiʻe, i kuʻu iho ai i ka waihona ipu,

β - ka huina ma ka apex,

a - aoao.

Maikaʻi isosceles triangle

Loa hana hoihoi 'waiwai i ke triangle, ka apex o ka i mea like i 90 degere. ka noonoo pono-huina triangle ABC. Like i loko o kekahi palapala hoopii, WA - kiekie i ke kumu.

Ke kumu pana pua e like. Ho omaulia i ko lakou nui hana,ʻaʻole e hana ai:

α = (180 - 90) / 2.

Penei, kihi Aia ma ka waihona ipu, mau i 45 degere. Ano, noonoo ADV triangle. He i mea mau huinahń loa. Mākou i loaʻa i ka huina AED. Ma na mea helu, ua loaa 45 degere. A, nolaila, keia triangle mea ole wale pono, akā, i ka isosceles. Nāʻaoʻao AD a me VD i na aoao, a ua like.

Akāʻaoʻao AD i ka ia manawa o ka hapalua o ka AU. Ua huli mai ia i loko o ke kiekie o ka equilateral triangle, ua like no ka hapalua o ka waihona ipu, me he mea kākau i loko o ka palapala o ka haʻilula, ua loaa ka mea kēia hōʻike:

H = i / 2.

Ka mea, e ole e poina i keia haʻilula mea wale nō i ka kūikawā hihia, a ua hiki ke hoʻohana wale no ka mea huinahń isosceles triangle mauna.

The Golden triangle

Loa hana hoihoi 'o ke gula triangle. Ma keia huahelu, o ka lākiō o kaʻaoʻao o ka waihona ipu, ua like ia i ka nui, i kapaia ma ka helu o Phidias. Kihi Aia ma ka luna - 36 degere, a me ka waihona ipu - 72 degere. Kēia triangle mahalo Pythagoreans. Golden triangle kumu lilo i kumu o ke iiiaanoaa o make ole masterpieces. Ka pono-ike elima-kuhikuhi mai la lakou hoku i kūkuluʻia ma ke kuʻina o isosceles triangle mauna. No ka mea, he nui na hana o Leonardo ka Vinci hoʻohana i ka loina o ke "gula triangle". Haku mele 'ana "Mona Lisa" ua ma muli e ma luna o nā kiʻi, a ho okumu i ka pentagram pono.

Pena "Cubism", hana kekahi o Pablo Pikasso, kupaianaha e nānā ke kumu o ka isosceles triangle.