Daim duab peb sab yog ib qho ntawm cov duab geometric feem ntau, uas peb twb tau paub hauv tsev kawm ntawv theem pib. Cov lus nug ntawm yuav ua li cas nrhiav thaj tsam ntawm daim duab peb sab yog ntsib los ntawm txhua tus tub ntxhais kawm hauv cov tshooj lus geometry. Yog li, dab tsi yog cov yam ntxwv ntawm kev nrhiav thaj chaw ntawm daim duab tuaj yeem paub qhov txawv? Hauv tsab xov xwm no, peb yuav xav txog cov qauv tsim nyog los ua kom tiav cov haujlwm no, nrog rau kev txheeb xyuas cov duab peb sab.
Tim duab peb sab
Koj tuaj yeem pom thaj tsam ntawm daim duab peb sab hauv txoj kev sib txawv kiag li, vim tias hauv geometry muaj ntau tshaj ib hom duab uas muaj peb lub kaum ntse ntse. Cov hom no suav nrog:
- Acute triangle.
- obt-angled.
- Equilateral (yog).
- daim duab peb sab.
- Isosceles.
Cia peb saib kom ze rau txhua yam ntawm daim duab peb sab uas twb muaj lawm.
Nyobdaim duab peb sab
Xws li daim duab geometric yog suav tias yog feem ntau hauv kev daws teeb meem geometric. Thaum nws tsim nyog los kos daim duab peb sab, qhov kev xaiv no los rau kev cawm.
Nyob rau hauv daim duab peb sab, raws li lub npe qhia, txhua lub kaum sab xis yog mob thiab ntxiv mus txog 180 °.
Obt-angled daim duab peb sab
Daim duab peb sab no kuj muaj ntau heev, tab sis muaj me ntsis tsawg dua qhov mob-angled. Piv txwv li, thaum daws cov duab peb sab (uas yog, koj paub ob peb ntawm nws sab thiab cov ces kaum thiab koj yuav tsum nrhiav cov ntsiab lus ntxiv), qee zaum koj yuav tsum txiav txim siab seb lub kaum sab xis yog obtuse lossis tsis. Lub cosine ntawm obtuse lub kaum sab xis yog tus lej tsis zoo.
Nyob rau hauv daim duab peb sab obtuse, tus nqi ntawm ib lub kaum sab xis tshaj 90 °, yog li ob lub ces kaum ntxiv tuaj yeem siv qhov me me (piv txwv li, 15 ° lossis txawm 3 °).
Yuav kom pom thaj tsam ntawm daim duab peb sab ntawm hom no, koj yuav tsum paub qee qhov nuances, uas peb yuav tham txog tom qab.
Nco thiab isosceles daim duab peb sab
Ib lub polygon tsis tu ncua yog ib daim duab uas suav nrog n cov ces kaum thiab txhua sab thiab kaum sib npaug. Qhov no yog daim duab peb sab. Txij li cov sum ntawm tag nrho cov kaum ntawm ib daim duab peb sab yog 180 °, txhua ntawm peb lub ces kaum yog 60 °.
Ib daim duab peb sab tsis tu ncua, vim nws cov cuab yeej, kuj hu ua ib daim duab sib npaug.
Nws tseem tsim nyog sau cia hauvdaim duab peb sab tsis tu ncua tsuas yog sau nrog ib lub voj voog thiab tsuas yog ib lub voj voog tuaj yeem ncig ncig nws, thiab lawv cov chaw nyob ntawm ib qho chaw.
Dhau li ntawm hom sib npaug, ib tus tuaj yeem xaiv ib daim duab peb sab isosceles, uas txawv me ntsis ntawm nws. Nyob rau hauv xws li ib daim duab peb sab, ob sab thiab ob lub kaum sab xis yog sib npaug zos rau ib leeg, thiab lub thib peb sab (kom cov ces kaum sib npaug zos adjoin) yog lub hauv paus.
Daim duab qhia txog daim duab peb sab isosceles DEF, cov ces kaum D thiab F uas sib npaug, thiab DF yog lub hauv paus.
daim duab peb sab
Ib lub kaum sab xis yog lub npe vim tias ib qho ntawm nws lub kaum sab xis yog lub kaum sab xis, uas yog, sib npaug li 90 °. Lwm ob lub kaum sab xis ntxiv txog 90°.
Qhov loj tshaj plaws ntawm daim duab peb sab, dag ntawm lub kaum sab xis ntawm 90 °, yog lub hypotenuse, thaum ob sab ntawm nws ob sab yog ob txhais ceg. Rau hom duab peb sab no, Pythagorean theorem siv tau:
Tus lej ntawm cov squares ntawm qhov ntev ntawm ob txhais ceg yog sib npaug rau cov square ntawm qhov ntev ntawm lub hypotenuse.
Daim duab qhia ib daim duab peb sab BAC nrog hypotenuse AC thiab ceg AB thiab BC.
Yuav kom pom thaj tsam ntawm daim duab peb sab nrog lub kaum sab xis, koj yuav tsum paub cov lej ntawm nws ob txhais ceg.
Cia peb mus rau cov qauv txhawm rau nrhiav thaj chaw ntawm daim duab no.
Basic area formulas
Nyob rau hauv geometry, muaj ob lub qauv uas tsim nyog rau kev nrhiav thaj tsam ntawm feem ntau ntawm cov duab peb sab, uas yog rau qhov mob-angled, obtuse-angled, tsis tu ncua thiabisosceles daim duab peb sab. Cia peb tsom xam txhua tus.
Cov mis no yog universal rau nrhiav thaj chaw ntawm daim duab peb tab tom txiav txim siab. Ua li no, nws yog txaus kom paub qhov ntev ntawm sab thiab qhov ntev ntawm qhov siab kos rau nws. Cov mis nws tus kheej (ib nrab ntawm cov khoom ntawm lub hauv paus thiab qhov siab) zoo li no:
S=½AH, qhov twg A yog sab ntawm daim duab peb sab thiab H yog qhov siab ntawm daim duab peb sab.
Piv txwv li, txhawm rau nrhiav thaj tsam ntawm daim duab peb sab-lub kaum sab xis ACB, koj yuav tsum muab nws sab AB los ntawm qhov siab CD thiab faib cov txiaj ntsig tau los ntawm ob.
Txawm li cas los xij, tsis yog ib qho yooj yim mus nrhiav thaj tsam ntawm daim duab peb sab li no. Piv txwv li, siv cov qauv no rau daim duab peb sab obtuse-angled, koj yuav tsum txuas ntxiv ib qho ntawm nws sab thiab tsuas yog tom qab ntawd kos qhov siab rau nws.
Hauv kev xyaum, cov qauv no siv ntau dua li lwm tus.
Ntawm ob sab thiab kaum
Cov mis no, zoo li yav dhau los, yog qhov tsim nyog rau feem ntau daim duab peb sab thiab hauv nws lub ntsiab lus yog qhov tshwm sim ntawm cov qauv rau kev nrhiav thaj tsam ntawm sab thiab qhov siab ntawm daim duab peb sab. Ntawd yog, cov qauv hauv qab kev txiav txim siab tuaj yeem yooj yim muab tau los ntawm yav dhau los. Nws cov lus zoo li no:
S=½sinOAB, qhov twg A thiab B yog sab ntawm daim duab peb sab thiab O yog lub kaum sab xis ntawm sab A thiab B.
Nco ntsoov tias lub sine ntawm lub kaum sab xis tuaj yeem pom hauv lub rooj tshwj xeeb uas muaj npe tom qab tus kws ua lej zoo Soviet V. M. Bradis.
Thiab tam sim no cia peb mus rau lwm cov qauv,haum tsuas yog rau cov hom peb sab tshwj xeeb.
Tshaj tawm ntawm ib daim duab peb sab
Ntxiv rau cov qauv thoob ntiaj teb, uas suav nrog qhov xav tau kos qhov siab hauv daim duab peb sab, thaj tsam ntawm daim duab peb sab uas muaj lub kaum sab xis tuaj yeem pom los ntawm nws ob txhais ceg.
Yog li, thaj tsam ntawm daim duab peb sab uas muaj lub kaum sab xis yog ib nrab ntawm cov khoom ntawm nws ob txhais ceg, lossis:
S=½ab, qhov twg a thiab b yog ob txhais ceg ntawm daim duab peb sab.
Daim duab peb sab
Hom duab geometric no txawv ntawm nws thaj chaw tuaj yeem pom nrog tus nqi teev ntawm tsuas yog ib sab ntawm nws sab (vim txhua sab ntawm daim duab peb sab sib npaug). Yog li, tau ntsib nrog txoj haujlwm ntawm "nrhiav thaj tsam ntawm daim duab peb sab thaum ob sab sib npaug", koj yuav tsum siv cov qauv hauv qab no:
S=A2√3 / 4, qhov twg A yog sab ntawm daim duab peb sab sib npaug.
Heron's Formula
Qhov kev xaiv kawg rau kev nrhiav thaj chaw ntawm daim duab peb sab yog Heron tus qauv. Txhawm rau siv nws, koj yuav tsum paub qhov ntev ntawm peb sab ntawm daim duab. Heron tus qauv zoo li no:
S=√p (p - a) (p - b) (p - c), qhov twg a, b thiab c yog ob sab ntawm daim duab peb sab.
Qee zaum txoj haujlwm tau muab: "qhov chaw ntawm daim duab peb sab tsis tu ncua - nrhiav qhov ntev ntawm nws sab." Nyob rau hauv rooj plaub no, koj yuav tsum tau siv cov qauv uas twb paub lawm los nrhiav thaj tsam ntawm daim duab peb sab tsis tu ncua thiab muab tus nqi ntawm sab (los yog nws cov square) los ntawm nws:
A2=4S / √3.
Exam Problems
Hauv GIA cov haujlwmMuaj ntau cov qauv hauv lej. Tsis tas li ntawd, feem ntau yuav tsum nrhiav thaj tsam ntawm daim duab peb sab ntawm daim ntawv checkered.
Hauv qhov no, nws yooj yim tshaj plaws los kos qhov siab rau ib sab ntawm daim duab, txiav txim siab nws qhov ntev los ntawm cov hlwb thiab siv cov qauv thoob ntiaj teb los nrhiav thaj chaw:
S=½AH.
Yog li, tom qab kawm cov qauv qhia hauv kab lus, koj yuav tsis muaj teeb meem nrhiav thaj tsam ntawm daim duab peb sab ntawm txhua yam.
