Daim duab peb sab: lub tswv yim thiab cov khoom

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2023-12-17 05:28

Kev daws teeb meem geometric yuav tsum muaj kev paub ntau. Ib qho ntawm cov ntsiab lus txhais ntawm qhov kev tshawb fawb no yog daim duab peb sab txoj cai.

Lub tswv yim no txhais tau tias daim duab geometric muaj peb lub kaum ntse ntse thiab

sides, thiab tus nqi ntawm ib lub kaum sab xis yog 90 degrees. Cov sab uas ua rau lub kaum sab xis yog hu ua ob txhais ceg, thaum lub thib peb sab uas yog opposite nws yog hu ua lub hypotenuse.

Yog tias ob txhais ceg hauv daim duab no sib npaug, nws yog hu ua isosceles txoj cai daim duab peb sab. Nyob rau hauv cov ntaub ntawv no, muaj ib tug teej tug mus rau ob hom ntawm daim duab peb sab, uas txhais tau hais tias cov khoom ntawm ob pawg yog soj ntsuam. Nco qab tias cov ces kaum ntawm lub hauv paus ntawm daim duab peb sab isosceles yeej ib txwm sib npaug, yog li ntawd, cov kaum sab xis ntawm daim duab no yuav suav nrog 45 degrees txhua.

Qhov muaj ntawm ib qho ntawm cov khoom hauv qab no tso cai rau peb lees paub tias ib daim duab peb sab yog sib npaug rau lwm qhov:

1. ob txhais ceg ntawm ob daim duab peb sab sib npaug;
2. daim duab muaj tib lub hypotenuse thiab ib ceg;
3. lub hypotenuse thiab lwm yamlos ntawm cov ces kaum ntse;
4. qhov xwm txheej ntawm kev sib npaug ntawm ceg thiab lub kaum sab xis raug pom.

Thaj chaw ntawm daim duab peb sab yog yooj yim xam ob qho tib si siv cov qauv qauv thiab raws li tus nqi sib npaug ntawm ib nrab ntawm cov khoom ntawm nws ob txhais ceg.

Cov piv txwv hauv qab no tau pom nyob rau hauv daim duab peb sab txoj cai:

1. txhais ceg tsis muaj dab tsi tab sis qhov txhais tau tias sib npaug rau qhov hypotenuse thiab nws qhov projection ntawm nws;
2. yog tias koj piav txog lub voj voog ncig ib daim duab peb sab, nws qhov chaw yuav nyob nruab nrab ntawm lub hypotenuse;
3. qhov siab kos los ntawm lub kaum sab xis yog qhov piv txwv piv rau qhov kev kwv yees ntawm ob txhais ceg ntawm daim duab peb sab mus rau nws qhov hypotenuse.

Nws yog qhov nthuav tias txawm tias daim duab peb sab yog dab tsi, cov khoom no yeej ib txwm pom.

Pythagorean theorem

Ntxiv rau cov khoom saum toj no, txoj cai peb sab yog cov yam ntxwv hauv qab no: lub square ntawm lub hypotenuse yog sib npaug rau cov lej ntawm cov plaub fab ntawm ob txhais ceg.

Txoj kev xav no yog lub npe tom qab nws tus tsim - Pythagorean theorem. Nws nrhiav pom qhov kev sib raug zoo no thaum nws tab tom kawm txog cov khoom ntawm cov squares ua rau ntawm ob sab ntawm daim duab peb sab.

Yuav ua pov thawj lub theorem, peb tsim ib daim duab peb sab ABC, nws ob txhais ceg peb denote a thiab b, thiab lub hypotenuse c. Tom ntej no, peb yuav tsim ob squares. Ib sab yuav yog hypotenuse, lwm qhov suav ntawm ob ceg.

Tom qab ntawd thaj tsam ntawm thawj square tuaj yeem pom nyob rau hauv ob txoj kev: raws li cov lej ntawm thaj tsam ntawm plaubdaim duab peb sab ABC thiab lub thib ob square, los yog raws li lub square ntawm sab, nws yog ntuj uas cov ratios yuav sib npaug. Ntawd yog:

с² + 4 (ab/2)=(a + b)^{2, hloov pauv qhov tshwm sim:}

c²+2 ab=a² + b^{2 + 2 ab}

Vim li ntawd, peb tau txais: c²=a² + b²

Yog li, daim duab geometric ntawm daim duab peb sab sab xis tsis yog tsuas yog rau tag nrho cov khoom yam ntxwv ntawm daim duab peb sab. Lub xub ntiag ntawm lub kaum sab xis ua rau qhov tseeb tias daim duab muaj lwm yam kev sib raug zoo tshwj xeeb. Lawv txoj kev kawm no muaj txiaj ntsig tsis yog hauv kev tshawb fawb nkaus xwb, tab sis kuj tseem nyob hauv lub neej niaj hnub, vim tias cov duab zoo li lub kaum sab xis pom muaj nyob txhua qhov chaw.