Thales' theorem: tsim thiab piv txwv ntawm kev daws qhov teeb meem

Hauv kev tshaj tawm no, peb yuav xav txog ib qho ntawm cov ntsiab lus tseem ceeb hauv chav kawm 8 geometry - Thales theorem, uas tau txais lub npe zoo li no los ntawm Greek lej thiab tus kws sau paj lug Thales ntawm Miletus. Peb tseem yuav tshuaj xyuas ib qho piv txwv ntawm kev daws qhov teeb meem los sib sau ua ke cov khoom uas tau nthuav tawm.

Nqe lus ntawm lub theorem

Yog tias qhov sib npaug sib npaug raug ntsuas ntawm ib qho ntawm ob txoj kab ncaj nraim thiab cov kab sib luag tau kos los ntawm lawv qhov kawg, ces hla txoj kab thib ob lawv yuav txiav tawm ntu sib npaug rau ib leeg.

• A₁A₂ =A₂A₃ ...
• B₁B₂ =B₂B₃ ...

Nco ntsoov: Qhov kev sib tshuam ntawm cov secants tsis ua lub luag haujlwm, piv txwv li lub theorem muaj tseeb ob qho tib si rau cov kab sib tshuam thiab rau cov kab sib txuas. Qhov chaw ntawm cov ntu ntawm cov ntu tseem tsis tseem ceeb.

Generalized formulation

Thales' theorem yog ib rooj plaub tshwj xeeb proportional ntu theorems *: parallel kab txiav proportional ntu ntawm secants.

Raws li qhov no, rau peb daim duab saum toj no, qhov sib npaug hauv qab no yog qhov tseeb:

* vim hais tias sib npaug ntu, suav nrog, yog proportional nrog tus coefficient ntawm proportionality sib npaug rau ib.

Inverse Thales theorem

1. Rau kev sib tshuam secants

Yog hais tias cov kab sib tshuam ob lwm kab (kab ib los yog tsis) thiab txiav tawm sib npaug los yog proportional ntu ntawm lawv, pib los ntawm sab saum toj, ces cov kab no yog parallel.

Los ntawm inverse theorem raws li nram no:

Yam yuav tsum tau muaj: sib npaug ntu yuav tsum pib los ntawm sab saum toj.

2. Rau parallel secants

Cov ntu ntawm ob ntu yuav tsum sib npaug rau ib leeg. Tsuas yog nyob rau hauv rooj plaub no lub theorem yog siv tau.

• a || b
• A₁A₂ =B₁B₂ =A₂A₃ =B₂B₃ ...

Piv txwv ntawm qhov teeb meem

Muab ib ntu AB ntawm qhov chaw. Faib nws mus rau 3 qhov sib npaug.

tshuaj

Kos los ntawm ib qho chaw A ncaj qha a thiab kos rau nws peb ntu sib law liag: AC, CD и DE.

point heev E ntawm txoj kab ncaj nraim a txuas nrog dot B ntawm ntu. Tom qab ntawd, los ntawm cov ntsiab lus ntxiv C и D thaum uas tig mus BE kos ob kab uas hla ntu AB.

Cov ntsiab lus ntawm kev sib tshuam tsim nyob rau hauv txoj kev no ntawm ntu AB faib ua peb qhov sib npaug (raws li Thales theorem).