Txawm tias nyob hauv tebchaws Iziv thaum ub, kev tshawb fawb tau tshwm sim, nrog kev pab los ntawm kev ntsuas qhov ntim, thaj chaw thiab lwm qhov ntau. Lub impetus rau qhov no yog kev tsim kho ntawm lub pyramids. Nws koom nrog ib tug loj tus naj npawb ntawm complex xam. Thiab ntxiv rau kev tsim kho, nws yog ib qho tseem ceeb kom ntsuas thaj av kom raug. Yog li kev tshawb fawb ntawm "geometry" tshwm sim los ntawm Greek lo lus "geos" - lub ntiaj teb thiab "metrio" - Kuv ntsuas.
Kev kawm ntawm cov ntawv geometric tau yooj yim los ntawm kev soj ntsuam ntawm astronomical phenomena. Thiab twb nyob rau hauv lub xyoo pua 17th BC. e. thawj txoj hauv kev los xam cov cheeb tsam ntawm ib lub voj voog, qhov ntim ntawm ib lub pob tau pom, thiab qhov kev tshawb pom tseem ceeb tshaj plaws yog Pythagorean theorem.
nqe lus ntawm txoj kev xav txog lub voj voog sau hauv daim duab peb sab yog raws li hauv qab no:
Tsuas yog ib lub voj voog tuaj yeem sau rau hauv daim duab peb sab.
Nrog qhov kev npaj no, lub voj voog tau sau, thiab daim duab peb sab yog ncig ze ntawm lub voj voog.
Nqe lus ntawm txoj kev xav txog qhov nruab nrab ntawm lub voj voog sau hauv daim duab peb sab yog raws li hauv qab no:
Central point of a circle inscribed indaim duab peb sab, muaj qhov taw tes ntawm kev sib tshuam ntawm bisectors ntawm daim duab peb sab.
Vajvoog sau nyob rau hauv daim duab peb sab isosceles
Ib lub voj voog raug suav hais tias yog sau rau hauv daim duab peb sab yog tias nws kov tag nrho nws sab nrog yam tsawg kawg nkaus.
Daim duab hauv qab no qhia txog lub voj voog hauv daim duab peb sab isosceles. Qhov xwm txheej ntawm lub theorem hais txog lub voj voog uas tau sau rau hauv daim duab peb sab - nws kov txhua sab ntawm daim duab peb sab AB, BC, thiab CA ntawm cov ntsiab lus R, S, Q, feem.
Ib qho ntawm cov khoom ntawm daim duab peb sab isosceles yog tias lub voj voog inscribes bisects lub hauv paus los ntawm qhov chaw ntawm kev sib cuag (BS=SC), thiab lub vojvoog ntawm lub voj voog inscribed yog ib feem peb ntawm qhov siab ntawm daim duab peb sab (SP=AS/3).
Properties of the triangle incircle theorem:
- ntu los ntawm ib qho vertex ntawm daim duab peb sab mus rau cov ntsiab lus ntawm kev sib cuag nrog lub voj voog sib npaug. Hauv daim duab AR=AQ, BR=BS, CS=CQ.
- Lub vojvoog ntawm lub voj voog (sau) yog thaj chaw faib los ntawm ib nrab-ib puag ncig ntawm daim duab peb sab. Ua piv txwv, koj yuav tsum kos ib daim duab peb sab isosceles nrog tib tsab ntawv tsim raws li hauv daim duab, ntawm qhov ntev hauv qab no: puag BC \u003d 3 cm, qhov siab AS \u003d 2 cm, sab AB \u003d BC, raws li, tau txais ib 2.5 cm. Peb kos ib lub bisector los ntawm txhua lub ces kaum thiab qhia qhov chaw ntawm lawv txoj kev sib tshuam raws li P. Peb sau lub voj voog nrog lub vojvoog PS, qhov ntev ntawm qhov yuav tsum tau pom. Koj tuaj yeem pom thaj tsam ntawm daim duab peb sab los ntawm kev muab 1/2 ntawm lub hauv paus los ntawm qhov siab: S=1/2DCAS=1/232=3 cm 2 . Semiperimeterdaim duab peb sab yog sib npaug rau 1/2 ntawm cov sum ntawm tag nrho cov sab: P \u003d (AB + BC + SA) / 2 \u003d (2.5 + 3 + 2.5) / 2 \u003d 4 cm; PS=S / P=3/4=0.75 cm2, uas yog qhov tseeb tiag thaum ntsuas nrog tus kav. Raws li, cov cuab yeej ntawm theorem hais txog ib lub voj voog sau hauv daim duab peb sab yog qhov tseeb.
Lub voj voog sau nyob rau hauv daim duab peb sab xis
Rau ib daim duab peb sab nrog lub kaum sab xis, cov khoom ntawm daim duab peb sab inscribed lub voj voog theorem siv. Thiab, ntxiv rau, lub peev xwm los daws teeb meem nrog postulates ntawm Pythagorean theorem yog ntxiv.
Lub vojvoog ntawm lub voj voog inscribed hauv ib daim duab peb sab tuaj yeem txiav txim tau raws li hauv qab no: ntxiv qhov ntev ntawm ob txhais ceg, rho tus nqi ntawm hypotenuse thiab faib cov txiaj ntsig tau los ntawm 2.
Muaj cov qauv zoo uas yuav pab koj xam thaj tsam ntawm daim duab peb sab - muab qhov ib puag ncig los ntawm lub vojvoog ntawm lub voj voog uas sau rau hauv daim duab peb sab.
Formulation of the incircle theorem
Theorems txog inscribed thiab circumscribed cov nuj nqis yog ib qho tseem ceeb nyob rau hauv lub planimetry. Ib tug zoo li no:
Qhov nruab nrab ntawm lub voj voog sau nyob rau hauv daim duab peb sab yog qhov sib tshuam ntawm cov bisectors kos los ntawm nws cov ces kaum.
Daim duab hauv qab no qhia cov pov thawj ntawm qhov kev xav no. Qhov sib npaug ntawm cov ces kaum tau qhia, thiab, raws li, qhov sib npaug ntawm cov duab peb sab uas nyob ib sab.
Theorem hais txog qhov nruab nrab ntawm lub voj voog sau hauv daim duab peb sab
Lub voj voog ntawm lub voj voog sau hauv daim duab peb sab,kos rau cov ntsiab lus tangent yog perpendicular rau ob sab ntawm daim duab peb sab.
Txoj haujlwm "tsim lub theorem hais txog lub voj voog sau hauv daim duab peb sab" yuav tsum tsis txhob xav tsis thoob, vim qhov no yog ib qho ntawm cov kev paub yooj yim tshaj plaws hauv geometry uas koj yuav tsum tau ua kom tiav los daws ntau yam teeb meem hauv lub neej tiag tiag.
