Plaub voos plaub ntuj: lub tswvyim thiab khoom

Kev daws teeb meem ntawm geometric teeb meem yuav tsum tau loj npaum li cas ntawm kev paub. Ib qho kev txhais cov ntsiab lus ntawm qhov kev tshawb fawb no yog ib txoj cai-angled peb tog.

Nyob rau hauv cov tswvyim no yog meant lub geometrical daim duab uas muaj peb fab thiab Sides, thiab tus nqi ntawm ib qho ntawm cov ces kaum yog 90 degrees. Cov tog neeg tsim txoj cai kaum lub npe, ceg thib peb, uas tawm tsam nws, yog hu ua hypotenuse.

Yog hais tias ob txhais ceg nyob rau hauv daim duab no yog sib npaug, nws yog hu ua ib txoj cai daim duab peb sab. Nyob rau hauv cov ntaub ntawv no muaj ib tug koom nrog rau ob hom ntawm cov vajvoos peb sab, uas txhais tau tias cov khoom cai nyob rau hauv ob pawg. Nco qab tias cov ces kaum ntawm lub hauv paus ntawm ib daim duab peb ceg isosceles yog kiag li sib npaug zos, li ntawm cov ces kaum qhov ntsej muag yuav muaj xws li 45 degrees.

Lub xub ntiag ntawm cov khoom siv hauv qab no tso cai rau peb hais tias ib daim duab peb sab yog sib npaug rau lwm tus:

1. Ob ceg ntawm ob ceg yog sib npaug;
2. Cov duab muaj tib hom hypotenuse thiab ib yam ntawm cov ceg;
3. Sib npaug nrog cov hypotenuse thiab ib qho ntawm cov ces kaum;
4. Tus mob ntawm kev vaj huam sib luag ntawm ib ceg thiab muaj lub qhov muag pom.

Lub cheeb tsam ntawm txoj cai-angled peb tog tau yooj yim raug computed nrog kev pab los ntawm standard qauv, thiab raws li tus nqi sib npaug rau cov khoom ntawm nws cov ceg.

Hauv txoj cai-angled peb tog cov kev sib raug zoo nram qab no muaj kev pom zoo:

1. Lub cathet yog tsis muaj dab tsi tab sis qhov nruab nrab proportional hypotenuse thiab nws cov projection rau nws;
2. Yog tias peb piav txog lub voj voog nyob ib ncig ntawm txoj cai peb tog, nws lub chaw yuav nyob nruab nrab ntawm qhov kev ntsuas hypotenuse;
3. Qhov siab tau kos los ntawm txoj cai kaum yog qhov nruab nrab ntawm qhov nruab nrab ntawm daim duab ntawm daim duab peb sab rau nws cov ntshav.

Nws yog nthuav tias, txawm tias yog txoj cai-angled peb tog, cov khoom no yeej ib txwm pom.

Pythagorean Theorem

Ntxiv nrog rau cov khoom saum toj no rau cov duab plaub ceg kaum plaub, qhov mob hauv qab no yog qhov: lub xwmfab ntawm lub hypotenuse yog sib npaug rau cov lej ntawm cov plaub ceg ntawm cov ceg. Noorem no npe tom qab nws tus founder - theorem ntawm Pythagoras. Nws qhib no piv thaum koom nyob rau hauv kev kawm lub zog ntawm cov squares tsev rau ntawm qhov lub sab ntawm lub duab peb sab.

Los ua pov thawj rau theorem, peb tsim ib daim duab peb sab ABC, ob txhais ceg uas yog qhia los ntawm ib tug thiab b, thiab qhov hypotenuse c. Tom ntej, peb tsim ob lub kaum plaub. Ib sab yuav muaj ib qho hypotenuse, tus tod muaj tus lej ntawm ob txhais ceg.

Ces cheeb tsam ntawm thawj square yuav pom muaj nyob rau hauv ob txoj kev: raws li qhov sib npaug hauv thaj tsam ntawm plaub ceg kaum sab xis ABC thiab ob lub xwmfab, los yog raws li ib sab square, nws yog qhov tseeb tias cov qauv yuav sib npaug. Ntawd yog:

4 nrog ² + (b / 2) = (ib tug + b) ^2, hloov lub resulting qhia:

² +2 ab = ib tug ² + b ² + ab 2

Raws li ib tug tshwm sim, peb tau: c = ² + b ^{2 2}

Yog li, daim duab geometric ntawm ib txoj cai-angled peb tog tsuas tsis yog tas nrho cov yam ntxwv ntawm cov vaj tse ntawm cov vaj tse peb ceg. Lub xub ntiag ntawm txoj cai kaum coj mus rau qhov tseeb tias daim duab muaj lwm yam kev sib raug zoo. Lawv txoj kev tshawb no tseem ceeb tsis yog nyob hauv kev tshawb fawb, tab sis tseem nyob hauv lub neej txhua hnub, txij li ib lub duab ua daim duab peb sab, nyob txhua qhov chaw.