Ithiyori kaThales: ukwakheka kanye nesibonelo sokuxazulula inkinga

Kule ncwadi, sizocubungula enye yezinkolelo-mbono eziyinhloko ekilasini lesi-8 lejiyomethri - i-Thales theorem, eyathola igama elinjalo ngokuhlonishwa kwesazi sezibalo esingumGreki nesazi sefilosofi uThales waseMiletus. Sizophinde sihlaziye isibonelo sokuxazulula inkinga ukuze sihlanganise indaba ethulwayo.

Okuqukethwe

Isitatimende sethiyori

Uma izingxenye ezilinganayo zikalwa komunye wemigqa emibili eqondile futhi imigqa ehambisanayo idwetshwa emaphethelweni awo, bese weqa umugqa wesibili oqondile bazosika izingxenye ezilingana nomunye kuwo.

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

  • A1A2 =A2A3 ...
  • B1B2 =B2B3 ...

Qaphela: Ukuphambana kwama-secant akunandima, okungukuthi ithiyori iyiqiniso kokubili kwemigqa enqamulanayo nakweminye ehambisanayo. Indawo yamasegimenti kuma-secants nawo ayibalulekile.

Ukwakhiwa okuvamile

Ithiyori kaThales iyindaba ekhethekile amathiyori engxenye yesilinganiso*: imigqa ehambisanayo isika amasegimenti alinganayo kuma-secant.

Ngokuvumelana nalokhu, emdwebeni wethu ongenhla, ukulingana okulandelayo kuyiqiniso:

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

* ngenxa yokuthi amasegimenti alinganayo, okuhlanganisa, alingana ne-coefficient yokulinganisa elingana nokukodwa.

I-Inverse Thales theorem

1. Okokunqamula ama-secants

Uma imigqa inqamula eminye imigqa emibili (ehambisanayo noma cha) futhi inqamula izingxenye ezilinganayo noma ezilinganayo kuyo, iqala phezulu, le migqa iyahambisana.

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

Kusuka ku-inverse theorem kulandela:

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

Isimo esidingekayo: izingxenye ezilinganayo kufanele ziqale ukusuka phezulu.

2. Ngama-secant ahambisanayo

Amasegimenti kuwo womabili amasegimenti kufanele alingane. Kulokhu kuphela i-theorem iyasebenza.

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

  • a || b
  • A1A2 =B1B2 =A2A3 =B2B3 ...

Isibonelo senkinga

Inikezwe ingxenye AB ebusweni. Ihlukanise ibe izingxenye ezi-3 ezilinganayo.

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

Isixazululo

I-Thales theorem: ukwakhiwa kanye nesibonelo sokuxazulula inkinga

Dweba iphuzu A ngqo a bese umaka kuyo izingxenye ezintathu ezilinganayo ezilandelanayo: AC, CD и DE.

iphuzu ngokwedlulele E emgqeni oqondile a xhuma nechashazi B engxenyeni. Ngemva kwalokho, ngokusebenzisa amaphuzu asele C и D parallel BE dweba imigqa emibili enqamula ingxenye AB.

Amaphuzu okuhlangana akhiwe ngale ndlela engxenyeni engu-AB ayihlukanise ibe izingxenye ezintathu ezilinganayo (ngokuvumelana ne-Thales theorem).

shiya impendulo