Yuav ua li cas mus nrhiav tau lub qhov siab ntawm lub Trapezoid?

Nyob rau hauv peb lub neej ntau heev peb yuav tau nrog rau cov kev siv ntawm geometry nyob rau hauv kev xyaum, xws li siv. Ntawm cov feem ntau geometric duab, muaj trapeze. Thiab los xyuas kom meej tias peb tes num yog kev vam meej thiab zoo nkauj, koj yuav tsum kom thiab yog muab xam rau ntawm lub ntsiab rau xws li ib tug duab.

Yuav ua li cas yog ib tug Keystone? Qhov no convex quadrilateral uas muaj ib tug khub ntawm thaum uas tig mus sab, raug xa mus rau raws li lub hauv paus ntawm lub Trapezoid. Tiam sis muaj ob yam uas txuas cov thaj av. Lawv hu ua sab. Ib tug ntawm cov teeb meem uas muaj feem xyuam rau qhov no lub cev, nws yog: "Yuav ua li cas mus nrhiav tau lub qhov siab ntawm lub Trapezoid" Cia li xav tau them sai sai mus rau qhov siab - ib tug ya uas yuav txiav txim qhov kev ncua deb ntawm ib tug puag rau lwm tus. Muaj ob peb txoj kev los mus txiav txim qhov no deb, nyob ntawm lub npe hu zog.

1. Paub qhov ntau ntawm ob bases, b txhais lawv thiab k, raws li zoo raws li lub cheeb tsam ntawm lub Trapezoid. Siv cov paub qhov tseem ceeb mus nrhiav lub qhov siab ntawm lub Trapezoid, nyob rau hauv cov ntaub ntawv no yooj yim heev. Raws li yog lub npe hu los ntawm cov geometry, cov Trapezoid cheeb tsam yog xam raws li cov khoom ntawm ib nrab ntawm cov sum ntawm hauv paus thiab qhov siab. Los ntawm cov mis no nws yuav yooj yim neeg tus yam nqi. Ua li no, faib lub cheeb tsam nyob rau hauv ib nrab tus nqi ntawm cov thaj chaw. Nyob rau hauv cov mis yuav zoo li no:

S = ((b + k) / 2) * h, ntawm no h = S / ((b + k) / 2) = 2 * S / (b + k)

2. Paub tias ntev ntawm lub midline, peb txhais d, thiab square. Rau cov neeg uas tsis paub, rau hauv nruab nrab txoj kab yog qhov kev ncua deb ntawm lub midpoints ntawm lub sab. Yuav ua li cas mus nrhiav tau lub qhov siab ntawm lub Trapezoid nyob rau hauv cov ntaub ntawv no? Raws li rau vaj tse Trapezoid, rau hauv nruab nrab txoj kab sau raws nkaus Ii mus rau ib nrab tus nqi ntawm cov hauv paus, i.e. d = (b + k) / 2. Dua peb chaw uasi mus rau cov mis mos square. Hloov ib nrab tus nqi ntawm cov luj rau ntawm tus nqi ntawm cov middle kab, peb muab tau cov nram qab no:

S = d * h

Raws li yuav pom los ntawm cov mis tau yooj yim heev deduced qhov siab. Faib lub cheeb tsam nyob rau midline ntawm cov nqi, peb yuav nrhiav tau cov tsis paub hais tias muaj nuj nqis. Peb sau cov mis no:

h = S / d

3. Paub ntev ntawm ib sab ntawm (b) thiab lub kaum sab xis tsim ntawm uas sab thiab qhov loj tshaj plaws puag. Lo lus teb rau lo lus nug ntawm yuav ua li cas nrhiav tau qhov siab ntawm lub Trapezoid, yog tseem nyob rau hauv cov ntaub ntawv no. Xav txog Trapezoid abcd, qhov twg AB thiab CD yog cov sab sab, nyob rau AB = b. Qhov loj tshaj plaws hauv paus yog AD. Lub kaum tsim los ntawm AB thiab AD yog denoted α. Los ntawm taw tes B tso tawm hauv lub qhov siab h nyob rau hauv AD puag. Tam sim no xav txog lub resulting daim duab peb sab ABF, uas yog lub. Sab AB yog lub hypotenuse, thiab BF-lub ceg. Los ntawm cov vaj tse txoj cai daim duab peb sab piv cov nqi cathetus thiab lub hypotenuse sau raws nkaus Ii mus rau tus nqi ntawm cov sine ntawm lub kaum sab xis ntawm qhov opposite cathetus (BF). Yog li ntawd, xaiv cov saum toj no, los mus laij lub qhov siab ntawm lub Trapezoid muab tus nqi ntawm ib tug tej nam thiab sine ntawm lub kaum sab xis α. Nyob rau hauv ib lub mis no yog raws li nram no:

h = b * kev txhaum (α)

4. Ib yam li ntawd, cov ntaub ntawv yog hais tias tus paub me me ntawm lub sab thiab lub kaum sab xis denoted β, tsim ntawm uas sab thiab lub me hauv paus. Nyob rau hauv kev daws tej teeb meem, lub kaum sab xis ntawm ib sab ntawm ib tug paub qhov siab thiab yog muaj 90 ° - β. Los ntawm cov thaj chaw ntawm cov vajvoos peb sab - piv ntev cathetus thiab lub hypotenuse sau raws nkaus Ii lub cosine ntawm lub kaum sab xis situated nruab nrab ntawm lawv. Los ntawm cov mis no nws yog ib qho yooj yim mus deduce siab nqi:

h = b * cos (β-90 °)

5. Yuav ua li cas mus nrhiav tau lub qhov siab ntawm lub Trapezoid, yog hais tias paub xwb rau qhov voos kheej-kheej ntawm lub inscribed vajvoog? Los ntawm cov lus txhais ntawm lub vajvoog, nws txhawj xeeb ib tug taw tes ntawm txhua lub hauv paus. Nyob rau hauv tas li ntawd, cov ntsiab lus yog raws li qhov chaw ntawm lub voj voog. Los ntawm no nws hais ntxiv hais tias qhov kev ncua deb nruab nrab ntawm lawv yog cov kab uas hla, thiab nyob rau tib lub sij hawm, lub qhov siab ntawm lub Trapezoid. Nws zoo li no:

h = 2 * r

6. Feem ntau muaj cov kev pab raws qib uas yuav tsum tau mus nrhiav rau qhov siab ntawm ib tug ceskaum Trapezoid. Nco qab hais tias ib tug Trapezoid nrog sib npaug sab yog hu ua ib tug ceskaum. Yuav ua li cas mus nrhiav tau lub qhov siab ntawm lub ceskaum Trapezoid? Yog hais tias lub diagonals yog perpendicular siab yog sib npaug zos rau ib nrab ntawm cov sum ntawm cov kev bases.

Tab sis yuav ua li cas yog hais tias tus diagonals yog tsis perpendicular? Xav txog ib tug ceskaum Trapezoid abcd. Raws li nws cov khoom, cov kev bases yog mus tib seem. Los ntawm no nws hais ntxiv hais tias lub ces kaum nyob puag yuav sib npaug zos. Kos ob heights BF thiab CM. Raws li cov foregoing, nws yuav sib cav hais tias lub duab peb ceg ABF thiab DCM yog muaj sib npaug, uas yog, AF = DM = (AD - BC) / 2 = (BK) / 2. Tam sim no, raws li nyob rau hauv lub tej yam kev mob ntawm qhov teeb meem, txhais tau lub npe hu ntau, thiab ces nrhiav altitude, noj mus rau hauv tus account tag nrho cov khoom ntawm ib tug ceskaum Trapezoid.