E kuhikuhi i ka hakahaka

'O kahi laina ma'amau i ka hakahaka kekahi o nā mea nui ma ka ma'amau. Loa'a iā ia kahi helu pau'ole o nā mea kūlohelohe i nele i ka leo, kahi, lō'ihi, a me nā mea'ē a'e. Ke hana nei kēia mau mea'u'uku i ka waiwai o ka geometry a kapa'ia he mau helu.

'O ke laina pololei i ka ākea he like me ka mea i hana'ia ma luna o ka pīkole e kū nei. Me ke kōkua o ka no'ono'o, pono e helu i nā helu'elua. Ma waena o lākou, a me ka palena o ko lākou palena i ka launa'ole me ke kōkua o kahi luna, ua huki'ia kahi laina. 'O kēia ka laina pololei i ka māhele. Ma kēia laina, hiki iā'oe ke koho i kahi māhele a i'ole kahi helu. Hana like kēia mau hana me nā hana like i hana'ia ma kahi mokulele.

Ma ka ma'omika, aia nā axioms e pili ana i ka ho'ākāka o kahi laina. Eia kēia mau'ōlelo:

1. Ma o nā hi'ohi'ona maika'i'elua hiki ke huki i ho'okahi laina ho'okahi wale nō.

2. Aia kekahi mau helu ma'elua o nā laina'elua o kekahi laina. A laila, hiki iā mākou ke'ōlelo aku i loko o ia mea nā mea kaulike'ole a pau o ke aho.

Mahalo i kēia mau axioms, ua maopopo ke laina o ka laina ma ka mokulele ma kahi mokulele.

I ka Geometry, ua'ike'ia kekahi hihia. Kū ia i kēlā mau wahi i kahi laina pololei i ke kikowaena e'ike'ia ma muli o ke ku'ina o'elua mau'ano like'ole. He'oia'i'o ka'ōlelo: inā'elua mau'ano like'ole i loa'a i kahi ho'okahi'oihana ma'amau, a laila, he laina ma'amau ma'amau. Ma keia laina, a me ka poe a pau na 'Aʻohe-dimensional mea o kēia mau geometric kinona.

'O ka ho'ohui like'ana o nā laina pololei i ka hakahaka hiki ke loa'a nā koho'ē a'e. I nā hihia a kēlā me kēia mea, hiki ke ho'ohālikelike. 'O ia, ma kēia'ano, aia nā laina i kahi helu pau'ole o nā mea ma'amau.

'O nā laina i ka hakahaka hiki ke loa'a kahi helu ho'okahi. Ma kēiaʻano, kaʻikepili laina i loko o ka kekahi pelane ke aupuni 'o ekolu dimensional makahiki. Hiki i kēia hihia ke ho'omaopopo i ka'oki i waena o nā laina.

I ka loa'a'ana i kahi hakahaka, hiki ke ho'ohālike'ia nā laina. I kēia kūlana, aia lākou i loko o ka pā'ani ho'okahi a'a'ole e launa pū i loko o ka lō'ihi a pau.
Ma kahi laina, a ma kahi laina e pili pū ana me ia, e ho'opili pololei'ia kahi vector vector. Ho'ohana pinepine'ia kēia mana'o hana honua i ka ho'oholo'ana i nā pilikia like'ole. Ke ho'ohana nei i ka vele, hiki iā'oe ke ho'oholo i ke kuhikuhi o kahi laina pololei.
Hiki i nā lina ke ho'opili. I kēia hihia, aia lākou ma nā'ano like'ole. 'O kēia ho'onohonoho'ana e alaka'i i ka mana'o geometical o ka'oki e kau ana ma waena o nā laina pololei. Ho'okomo nui'ia ka nānā'ana i nā hihia o ka ho'onohonoho pono'ole o nā laina i'ekolu wahi. I loko o ia mau'ano ho'ohālikelike,'o ka'oki ma waena o lākou he waiwai e like me nā kanaiwakumamāiwa.

Hiki iā'oe ke kuhikuhi i kahi laina pololei i ka māhele ma nā'ano like'ole. No ka hana'ana i kēia,'ike ka'ike o ke axioms. Ke hele nei mai ka'ike'o kahi laina pololei ho'okahi wale nō e hiki ai ke komo i nā helu'elua i koho'ia i ka māhele, hiki iā mākou ke kaha palapala iā ia ma ke kau'ana i kahi laina ma o nā mea i ho'olālā'ia.

Inā kūpono ia e kūkulu i kahi mea kinona i loko o kahi pūnaewele ho'onohonoho o kahi'ano kikohā, kahi i loa'a i'ekolu wahi, a laila ua hana'ia kekahi'ano ho'ohālike. Ke ho'ohālikelike i kahi laina pololei, pono pono ke hilina'i i nā kikowaena o kona mau helu'elua, pono e'ike'ia.

Ke kūkulu'ia ka laina e pono ai, hiki iā mākou ke ho'ohana i ka'ōlelo like'ole. Ma kēia hihia, ma kahi o kekahi kikowaena'a'ole i kā mākou laina pololei, hiki iā mākou ke kūkulu i kēlā me kēia ki'i'ōmene, nā mea āpau a pau'ole e pili ana i ia mea.

'O ka mokulele a me ka laina i ke āpau paha e hiki ke pili ke'ano. No ke kūkulu'ana i kahi laina i kēia hopena, ua unuhi'ia kahi ki'i geometric. I kēia hihia,'o ka'oki o ka hui'ana o ia laina pololei a'o ka mokulele he 90 degrees.