Bisector ntawm ib tug daim duab peb sab thiab nws cov khoom

Ntawm cov ntau yam ntawm ob lub tsev kawm ntawv muaj xws li "geometry". Feeb ntau, nws yog ntseeg hais tias cov pog koob yawg koob ntawm no systematic science yog Greeks. Rau hnub tim, lub Greek geometry hu ua elementary, vim nws yog qhov pib ntawm txoj kev tshawb no ntawm qhov nyuaj cov ntaub ntawv: dav hlau, kab, tsis tu ncua uas thiab cov vajvoos peb sab. Thaum kawg peb yuav txiav koj cov xim, tab sis, theej rau lub bisector ntawm no daim duab. Rau cov neeg uas muaj tsis nco qab lawm, lub bisector ntawm ib tug peb tog yog ib tug ya bisector ntawm ib qho ntawm cov ces kaum ntawm ib tug daim duab peb sab, uas faib nws nyob rau hauv ib nrab thiab koom lub sab saum toj rau ib tug taw tes nyob rau sab nraud.

Daim duab peb sab Bisector muaj ib tug xov tooj ntawm cov khoom uas yuav tsum tau paub tias thaum twg soj ntsuam uas muaj tej yam teeb meem:

• Bisector nruab nrab yog cov locus ntawm cov ntsiab lus ntawm sib npaug zos mus tej thaj chaw deb ntawm lub ces kaum uas nyob ib sab mus rau lub sab.
• Bisector ntawm ib tug daim duab peb sab cais lub opposite sab ntawm lub ces kaum rau hauv feem uas yog xwm yeem mus rau ib sab sab. Piv txwv li, muab daim duab peb sab MKB, qhov twg K mus los ntawm ces kaum bisector txuas lub kab los sib ntsib ntawm lub kaum sab xis mus rau lub point A nyob rau sab nraud MB. Tom qab Ntsuam xyuas cov cuab yeej thiab peb daim duab peb sab, peb muaj MA / AB = MK / KB.
• Tus taw tes uas tshuam lub bisector ntawm peb cov ces kaum ntawm ib tug peb tog yog qhov chaw ntawm ib lub voj voog uas yog inscribed nyob rau hauv tib lub daim duab peb sab.
• Base bisectors ib sab nraud thiab nrog ob tug ces kaum yog nyob rau tib txoj kab ncaj nraim, muab hais tias cov sab nraud bisector ntawm lub kaum sab xis yog tsis thaum uas tig mus rau rov qab sab ntawm lub duab peb sab.
• Yog hais tias ob bisectors ntawm ib tug daim duab peb sab yog muaj sib npaug, ces tus daim duab peb sab yog ceskaum.

Nws yuav tsum tau muab sau tseg tias yog hais tias peb lub bisector, qhov kev siv ntawm ib tug peb tog rau lawv, txawm nrog kev pab los ntawm ib tug compass, nws yog tsis yooj yim sua.

Heev feem ntau thaum daws teeb meem bisector ntawm ib tug peb tog yog tsis paub, tab sis nws yog tsim nyog los mus txiav txim nws kav ntev npaum. Yuav kom daws tau qhov teeb meem no nws yog tsim nyog los paub lub kaum sab xis, uas yog muab faib nyob rau hauv ib nrab bisector ntawm, thiab nyob ib sab mus no ces kaum ntawm ib sab. Nyob rau hauv cov ntaub ntawv no, tus yam ntev yog txhais raws li tus piv ntawm ob zaug ntawm lub ces kaum uas nyob ib sab rau cov khoom sab thiab lub cosine ntawm lub kaum sab xis ntawm lub bisection mus rau lub sum ntawm sab uas nyob ib sab mus rau lub ces kaum. Piv txwv li, muab tag nrho cov tib MKB daim duab peb sab. Nws nyob rau hauv lub bisector ntawm lub kaum sab xis K thiab CF tshuam opposite sab tom A. Lub kaum sab xis ntawm uas tus bisector yog denoted y. Tam sim no peb sau tag nrho cov uas hais tias lus raws li ib tug noj mis nyuj tov: kos = (2 * MK * KB * cos y / 2) / (MK + KB).

Yog hais tias tus nqi ntawm lub kaum sab xis ntawm uas tus bisector ntawm daim duab peb sab, yog tsis paub, tab sis lub npe hu mus rau tag nrho nws cov sab, nyob rau hauv thiaj li yuav xam qhov ntev ntawm lub bisector, peb yuav siv ib tug ntxiv nce mus nce los, uas peb hu rau semiperimeter thiab denoted los ntawm tsab ntawv P: P = 1/2 * (MK + KB + MB). Ces ua ib co kev hloov nyob rau hauv lub saum toj no mis, uas yog txiav txim los ntawm lub bisector ntawm qhov ntev, namely, nyob rau hauv lub numerator teem ob zaug lub square hauv paus ntawm qhov khoom ntawm lub lengths ntawm lub sab nyob ib sab mus rau lub ces kaum, thiab nyob rau hauv particular semiperimeter qhov twg semiperimeter rho tawm los ntawm qhov ntev ntawm lub peb sab. Lub denominator yog tshuav unchanged. Nyob rau hauv cov mis mos daim ntawv no yuav tshwm sim li: kos = 2 * √ (MK * KB * P * (P-MB)) / (MK + KB).

Bisector ntawm lub cai daim duab peb sab muaj tib lub zog li nyob rau hauv li niaj zaus, tab sis, dua li cov neeg twb paub tias, muaj cov tshiab: bisector ntse fab ntawm cov kev tshuam ntawm ib lub duab peb sab tsim ib qho kaum sab xis ntawm 45 degrees. Yog hais tias tsim nyog, nws yog ib qho yooj yim los ua pov thawj, siv lub thaj chaw ntawm daim duab peb sab thiab lub nyob ib sab ces kaum.

Bisector ntawm ib tug ceskaum daim duab peb sab nrog tus zog thiab muaj ob peb ntawm nws tus kheej. Cia peb nco ntsoov hais tias nws yog rau daim duab peb sab. Xws li ib tug daim duab peb sab ob sab yog muaj sib npaug, thiab yog nyob ib sab mus rau lub hauv paus ces kaum. Nws hais ntxiv hais tias lub bisector, uas tog rau hauv sab ntawm ib tug ceskaum daim duab peb sab yog muaj sib npaug. Nyob rau hauv tas li ntawd, lub bisector, poob rau hauv lub substrate, thiab ib txhij lub siab thiab theem nrab.