Ma kēia paʻi ʻana, e noʻonoʻo mākou i kekahi o nā theorems nui ma ka papa 8 geometry - ka Thales theorem, i loaʻa i kēlā inoa i ka hanohano o ka Helene mathematician a me ke akeakamai ʻo Thales o Miletus. E kālailai pū mākou i kekahi laʻana o ka hoʻoponopono ʻana i ka pilikia e hoʻohui i nā mea i hōʻike ʻia.
ʻO ka ʻōlelo o ka theorem
Inā ana ʻia nā ʻāpana like ma kekahi o nā kaha pololei ʻelua a huki ʻia nā kaha like ʻole ma ko lākou mau welau, a laila e ʻaʻa i ka laina pololei ʻelua e ʻoki lākou i nā ʻāpana like me kekahi ma luna.
- A1A2 =A2A3 ...
- B1B2 =B2B3 ...
'Ōlelo Aʻo: ʻAʻole pili ka hui like ʻana o nā secant, ʻo ia hoʻi, ʻoiaʻiʻo ka theorem no nā laina ʻokoʻa a no nā laina like. ʻAʻole nui ka wahi o nā ʻāpana ma nā secants.
ʻO ka hoʻopuka hoʻolaha
He hihia kūikawā ʻo Thales' theorem nā kumukānāwai māhele kaulike*: ʻoki nā laina like ʻole i nā ʻāpana like ʻole ma nā secants.
I kulike ai me keia, no ko kakou kaha kii ana maluna, ua pololei keia like ana.
* no ka mea, ua kūlike nā ʻāpana like, me ka like me ka koena o ka like me hoʻokahi.
Theorem inverse Thales
1. No ka hui ʻana i nā ʻāpana
Inā hui nā laina i ʻelua mau kaha ʻē aʻe (like a ʻaʻole paha) a ʻoki i nā ʻāpana like a kūlike paha ma luna o lāua, e hoʻomaka ana mai luna mai, a laila ua like kēia mau laina.
Mai ka inverse theorem penei:
Kūlana pono: e hoʻomaka nā ʻāpana like mai luna mai.
2. No na pauku like
Pono e like nā ʻāpana o nā ʻāpana ʻelua me kekahi. Ma kēia hihia wale nō e pili ana ka theorem.
- a || b
- A1A2 =B1B2 =A2A3 =B2B3 ...
Laʻana o kahi pilikia
Hāʻawi ʻia i kahi ʻāpana AB ma luna o ka ʻili. E puunaue i 3 mau apana like.
pāʻoihana
E kaha mai kahi kiko A kauoha a a e kaha iho i ekolu mahele like. AC, CD и DE.
lae loa E ma ka laina pololei a pili me ke kiko B ma ka mahele. Ma hope o kēlā, ma nā wahi i koe C и D ʻano like BE e kaha i elua laina e oki i ka mahele AB.
ʻO nā kiko o ka hui ʻana i hana ʻia ma kēia ʻano ma ka māhele AB e puʻunaue iā ia i ʻekolu mau ʻāpana like (e like me ka Thales theorem).