Kab pheeb ces kaum equilateral Trapezoid. Yuav ua li cas yog qhov nruab nrab txoj kab ntawm lub Trapezoid. Hom trapezoids. Trapeze - nws ..

Trapeze - ib tug tshwj xeeb cov ntaub ntawv ntawm ib tug quadrangle, nyob rau hauv uas ib tug khub ntawm sab yog mus tib seem. Lub sij hawm "Trapezoid" yog muab tau los ntawm Greek lo lus τράπεζα, lub ntsiab lus "rooj", "rooj". Nyob rau hauv no tsab xov xwm peb yuav saib hom trapeze thiab nws cov khoom. Tsis tas li ntawd, peb saib yuav ua li cas los xam tus neeg hais ntawm lub geometrical daim duab. Piv txwv li, lub kab pheeb ces kaum ntawm ib tug equilateral trapezium, rau hauv nruab nrab txoj kab, cheeb tsam thiab lwm tus. Cov khoom muaj nyob rau hauv lub elementary geometry nrov style, t. E. Nyob rau hauv ib qho yooj yim mus siv cuag yam.

Txheej txheem cej luam

Ua ntej, peb to taub li cas ib tug quadrangle. Qhov no xam yog ib tug tshwj xeeb cov ntaub ntawv ntawm ib tug polygon muaj plaub sab thiab plaub vertices. Ob tug vertices ntawm ib tug quadrilateral, uas yog tsis nyob ib sab, hu ua opposite. Ib yam yuav hais tau ntawm lub ob uas tsis yog-nyob ib sab sab. Lub ntsiab yam ntawm quadrangles - ib tug parallelogram, duab plaub, rhombus, square, Trapezoid thiab deltoid.

Yog li ntawd rov qab mus rau lub trapeze. Raws li peb tau hais tias, qhov no daim duab ob sab yog mus tib seem. Lawv yog cov hu ua bases. Tus lwm yam ob (non-thaum uas tig mus) - lub sab. Cov ntaub ntawv ntawm lub ntau yam xeem thiab xeem ntau heev koj yuav ua tau raws txoj kev sib tw txuam nrog trapezoids uas nws tshuaj feem ntau yuav tsum tau cov tub ntxhais kawm ntawv txoj kev paub tsis them los ntawm qhov kev pab cuam. Lub tsev kawm ntawv thaum kawg geometry qhia cov menyuam kawm ntawv nrog cov ces kaum zog thiab diagonals li zoo raws li lub nruab nrab txoj kab ntawm ib tug ceskaum Trapezoid. Tab sis lwm yam tshaj li hais tias xa mus rau ib tug duab zoo muaj lwm nta. Tiam sis hais txog lawv yav tom ntej ...

hom trapeze

Muaj ntau ntau hom no daim duab. Txawm li cas los, feem ntau txoj kev cai uas yuav tau xav txog ob ntawm lawv - ceskaum thiab lub.

1. lub Trapezoid - ib daim duab nyob rau hauv uas yog ib tug ntawm lub sab perpendicular mus rau lub hauv paus. Nws muaj ob tug ces kaum yeej ib txwm sib npaug zos rau cuaj caum degrees.

2. ceskaum trapezium - ib tug duab daim duab uas nws sab yog muaj sib npaug. Yog li ntawd, thiab cov ces kaum nyob puag kuj yog muaj sib npaug.

Lub ntsiab ntsiab cai ntawm txoj kev rau kev kawm lub zog ntawm cov Trapezoid

Cov yooj yim hauv paus ntsiab lus muaj xws li cov kev siv ntawm thiaj li hu ua hauj lwm mus kom ze. Nyob rau hauv qhov tseeb, yog tsis muaj yuav tsum tau mus nkag rau hauv ib tug theoretical kawg Geometry tshiab thaj chaw ntawm no daim duab. Lawv muaj peev xwm yuav qhib los yog nyob rau hauv tus txheej txheem ntawm formulating rau ntau yam kev pab raws qib (zoo dua system). Nws tseem ceeb heev uas tus kws qhia ntawv paub tias dab tsi paub tab uas koj yuav tau muab nyob rau hauv pem hauv ntej ntawm cov tub ntxhais kawm thaum twg muab lub sij hawm ntawm txoj kev kawm. Ntxiv mus, txhua Trapezoid vaj tse yuav tsum sawv cev raws li ib tug tseem ceeb ua hauj lwm nyob rau hauv lub ua hauj lwm system.

Lub hauv paus ntsiab yog li no-hu ua kauv koom haum ntawm txoj kev tshawb "zoo kawg li" trapeze zog. Qhov no implies ib tug rov qab mus rau tus txheej txheem ntawm kev kawm rau tus neeg nta ntawm lub geometric duab. Yog li, cov menyuam kawm ntawv yooj yim rau koj nco ntsoov lawv. Piv txwv li, cov cuab yeej ntawm cov plaub cov ntsiab lus. Nws yuav muaj pov thawj raws li nyob rau hauv txoj kev tshawb no ntawm kev zoo sib thooj thiab tom qab siv vectors. Ib tug Vaj Huam Sib Luag cov vajvoos peb sab uas nyob ib sab mus rau lub sab ntawm daim duab, nws yog ua tau los ua pov thawj los ntawm kev siv tsis tau tsuas yog lub thaj chaw ntawm cov vajvoos peb sab sib npaug zos heights nrhiav tau tus sab uas dag rau ib tug ncaj kab, tab sis kuj los ntawm kev siv cov mis S = 1/2 (b * sinα). Tsis tas li ntawd, nws tseem tau mus ua hauj lwm tawm kev cai lij choj ntawm sines rau lub inscribed trapezium los yog txoj cai-angled daim duab peb sab thiab Trapezoid piav nyob rau hauv t. D.

Txoj kev siv "cov" nta ib tug duab daim duab nyob rau hauv cov ntsiab lus ntawm lub tsev kawm ntawv chav kawm - ib tug tasking lawv technology qhia. Qhov kev siv rau kawm lub zog ntawm cov tso cai ntawm lub lwm yam tso cai cov menyuam kawm ntawv kawm cov trapeze ntxaum thiab kom txoj kev vam meej ntawm neeg ua hauj lwm. Yog li ntawd, peb npaj mus rau txoj kev tshawb no ntawm no zoo kawg li daim duab.

Hais thiab cov khoom ntawm ib tug ceskaum Trapezoid

Raws li peb tau sau tseg, nyob rau hauv no geometric duab sab yog muaj sib npaug. Tsis tau nws yog lub npe hu raws li ib tug txoj cai Trapezoid. Thiab yog dab tsi nws thiaj li zoo kawg li thiab vim li cas tau txais nws lub npe? Qhov tshwj xeeb nta ntawm no daim duab txog hais tias nws muaj tsis tau tsuas yog sib npaug zos sab thiab ces kaum nyob puag, tab sis kuj diagonally. Nyob rau hauv tas li ntawd, lub sum ntawm cov ces kaum ntawm ib ceskaum Trapezoid yog sib npaug zos rau 360 degrees. Tab sis hais tias tsis yog tag nrho cov! Tsuas yog nyob ib ncig ntawm ceskaum yuav tau piav los ib lub voj voog ntawm tag nrho cov paub trapezoids. Qhov no yog vim lub fact tias lub sum ntawm opposite ces kaum nyob rau hauv no daim duab yog 180 degrees, thiab tsuas yog nyob rau hauv tus mob no yuav piav raws li ib lub voj voog ib ncig ntawm lub quadrangle. Cov nram qab no thaj chaw ntawm lub geometric duab no yog hais tias qhov kev ncua deb ntawm lub sab saum toj ntawm lub hauv paus mus rau lub projection ntawm lub tawm tsam peaks ntawm txoj kab uas muaj qhov no los luj yuav ua ncaj rau cov midline.

Tam sim no cia saib yuav ua li cas nrhiav tau cov chaw ti ntawm ib tug ceskaum Trapezoid. Xav txog ib tug daws qhov teeb meem no, muab hais tias qhov luaj li cas ntawm ob tog paub daim duab.

kev txiav txim siab

Nws yog txoj kev cai uas mus txhais lub quadrangle cov tsiaj ntawv A, B, C, D, qhov twg BS thiab BP - lub hauv paus. Nyob rau hauv ib tug ceskaum Trapezoid sab yog muaj sib npaug. Peb hais tsis xav hais tias lawv loj yog sib npaug zos rau X thiab Y qhov ntev yog bases thiab Z (lesser thiab ntau dua, ntsig txog). Rau lub xam ntawm lub kaum sab xis ntawm lub yuav tsum tau siv nyob rau hauv lub qhov siab H. Cov no yog ib txoj cai-angled daim duab peb sab ABN qhov twg AB - lub hypotenuse, thiab BN thiab IB - ob txhais ceg. Xam qhov luaj li cas ntawm cov ceg IB: rho los ntawm cov loj los luj tsawg heev, thiab cov kev tshwm sim no tau muab faib los ntawm 2. sau ib lub mis: (ZY) / 2 = F. Tam sim no, los mus laij lub mob kaum sab xis ntawm daim duab peb sab siv muaj nuj nqi cos. Peb muab tau cov nram qab no nkag: cos (β) = X / F. Tam sim no xam lub kaum sab xis: β = Arcos (X / F). Ntxiv mus, kev paub txog ib tug kaum, peb yuav txiav txim thiab thib ob, yuav ua rau qhov no elementary xam lag luam: 180 - β. Tag nrho cov ces kaum yog txhais.

Muaj kuj yog ib tug thib ob tshuaj rau qhov teeb meem no. Thaum pib yog rho los ntawm cov ces kaum nyob rau hauv lub qhov siab ntawm tus ceg N. laij cov nqi ntawm cov BN. Peb paub hais tias cov square ntawm lub hypotenuse ntawm ib txoj cai daim duab peb sab yog sib npaug zos rau cov sum ntawm cov plaub fab ntawm lub ob sab. Peb tau txais: BN = √ (X 2 F2). Tom ntej no, peb siv lub trigonometric muaj nuj nqi TG. Cov no: β = arctg (BN / F). Cov mob lub yog pom. Tom ntej no, peb txhais tau ib tug obtuse angle li nyob rau hauv thawj txoj kev.

Cov cuab yeej ntawm tus diagonals ntawm ib tug ceskaum Trapezoid

Ua ntej, peb sau cov plaub cov kev cai. Yog hais tias lub kab pheeb ces kaum rau hauv ib qho ceskaum Trapezoid yog perpendicular, ces:

- rau qhov siab ntawm daim duab yog sib npaug zos rau qhov tawm ntawm cov hauv paus, muab faib los ntawm ob;

- nws qhov siab thiab qhov nruab nrab txoj kab yog muaj sib npaug;

- thaj tsam ntawm lub Trapezoid yog sib npaug zos rau cov square ntawm lub qhov siab (center kab mus rau ib nrab bases);

- lub square ntawm lub kab pheeb ces kaum ntawm ib tug square yog sib npaug zos rau ib nrab ntawm cov sum ntawm ob zaug lub square bases los yog midline (siab).

Tam sim no saib cov mis defining kab pheeb ces kaum ib tug equilateral Trapezoid. Qhov no daim ntawm cov ntaub ntawv yuav tsum tau muab faib ua plaub qhov chaw:

1. Formula kab pheeb ces kaum ntev los ntawm nws cov sab.

Peb hais tsis xav hais tias A yog - ib tug tsawg dua puag, B - Top, C - sib npaug zos sab, D - kab pheeb ces kaum. Nyob rau hauv cov ntaub ntawv no, qhov ntev yuav tsum tau txiav txim raws li nram no:

D = √ (C 2 + A * B).

2. Formula rau lub kab pheeb ces kaum ntev ntawm lub cosine.

Peb hais tsis xav hais tias A yog - ib tug tsawg dua puag, B - Top, C - sib npaug zos sab, D - kab pheeb ces kaum, α (nyob rau hauv sab puag) thiab β (lub sab sauv puag) - Trapezoid cov ces kaum. Peb muab tau cov nram qab no mis, los ntawm cov uas ib tug yuav xam qhov ntev ntawm lub kab pheeb ces kaum:

- D = √ (A2 + S2-2A * C * cosα);

- D = √ (A2 + S2-2A * C * cosβ);

- D = √ (B2 + S2-2V * C * cosβ);

- D = √ (B2 + S2-2V * C * cosα).

3. Formula kab pheeb ces kaum ntev ntawm ib ceskaum Trapezoid.

Peb hais tsis xav hais tias A yog - ib tug tsawg dua puag, B - sab sauv, D - kab pheeb ces kaum, M - nruab nrab txoj kab H - qhov siab, P - thaj tsam ntawm lub Trapezoid, α thiab β - lub kaum sab xis ntawm diagonals. Txiav txim seb qhov ntev ntawm lub nram qab no qauv:

- D = √ (M2 + N2);

- D = √ (H 2 + (A + B) 2/4);

- D = √ (N (A + B) / sinα) = √ (2n / sinα) = √ (2m * N / sinα).

Rau cov ntaub ntawv no, lub koob pheej ntawm lawv: sinα = sinβ.

4. Formula kab pheeb ces kaum ntev los ntawm lub sab thiab qhov siab.

Peb hais tsis xav hais tias A yog - ib tug tsawg dua puag, B - Top, C - sab, D - kab pheeb ces kaum, H - qhov siab, α - lub kaum sab xis nrog lub sab puag.

Txiav txim seb qhov ntev ntawm lub nram qab no qauv:

- D = √ (H 2 + (A-P * ctgα) 2);

- D = √ (H 2 + (B + F * ctgα) 2);

- D = √ (A2 + S2-2A * √ (C2-H2)).

Hais thiab cov khoom ntawm ib lub trapezium

Cia saib dab tsi yog xav nyob rau hauv no geometrical daim duab. Raws li peb tau hais tias, peb muaj ib lub Trapezoid ob txoj cai ces kaum.

Dhau li ntawm tus classical txhais, muaj lwm tus neeg. Piv txwv li, ib lub Trapezoid - ib tug Trapezoid nyob rau hauv uas ib sab yog lawv mus rau hauv lub hauv paus. Los yog puab muaj nyob rau ntawm lub sab ces kaum. Nyob rau hauv no hom ntawm trapezoids siab yog lub sab uas yog perpendicular mus rau lub bases. Qhov nruab nrab txoj kab - ib ya uas txuas lub midpoints ntawm ob sab. Cov cuab yeej ntawm hais tias lub caij yog hais tias nws yog thaum uas tig mus rau lub bases thiab sib npaug zos mus rau ib nrab ntawm lawv sum.

Tam sim no cia peb xav txog qhov yooj yim qauv uas txhais tau lub geometric duab. Ua li no, peb xav hais tias A thiab B - puag; C (perpendicular mus rau lub hauv paus) thiab D - sab ntawm lub lub trapezium, M - nruab nrab txoj kab, α - mob lub, P - cheeb tsam.

1. Lub sab perpendicular mus rau lub hauv paus, ib daim duab sib npaug zos rau qhov siab qhov (C = N), thiab sib npaug qhov ntev ntawm lub thib ob sab A thiab lub sine ntawm lub kaum sab xis α ntawm ib tug ntau dua puag (C = A * sinα). Ntxiv mus, nws yog sib npaug zos rau cov khoom ntawm lub tangent ntawm lub mob lub α thiab qhov sib txawv nyob rau hauv bases: C = (A-B) * tgα.

2. Cov sab D (tsis perpendicular mus rau lub hauv paus) sib npaug zos rau cov quotient ntawm qhov txawv ntawm A thiab B thiab cosine (α) los yog ib tug mob lub mus rau lub ntiag siab nuj nqis H thiab sine mob lub: A = (A-B) / cos α = C / sinα.

3. Cov sab uas yog perpendicular mus rau lub hauv paus, yog sib npaug zos rau cov square hauv paus ntawm qhov square ntawm qhov txawv D - lub thib ob sab - thiab ib tug square puag sib txawv:

C = √ (Q2 (A-B) 2).

4. Sab A lub Trapezoid yog sib npaug zos rau cov square hauv paus ntawm ib tug square sum ntawm ib tug square sab thiab C bases geometric zoo sib txawv: D = √ (C 2 + (A-B) 2).

5. Lub sab C yog sib npaug zos rau cov quotient ntawm lub square ob lub sum ntawm nws cov bases: C = P / M = 2P / (A + B).

6. Qhov chaw txhais los ntawm cov khoom M (qhov chaw kab ntawm lub lub Trapezoid) nyob rau hauv qhov siab los sab taw qhia perpendicular mus rau lub bases: P = M * N = M * C.

7. Txoj hauj lwm C yog tus quotient ntawm ob zaug lub square zoo los ntawm cov khoom sine mob kaum sab xis thiab lub sum ntawm nws cov bases: C = P / M * sinα = 2P / ((A + B) * sinα).

8. Formula sab ntawm ib lub trapezium los ntawm nws cov kab pheeb ces kaum, thiab lub kaum sab xis ntawm lawv:

- sinα = sinβ;

- C = (D1 * D2 / (A + B)) * sinα = (D1 * D2 / (A + B)) * sinβ,

qhov twg D1 thiab D2 - kab pheeb ces kaum ntawm lub Trapezoid; α thiab β - lub kaum sab xis ntawm lawv.

9. Formula sab ntawm lub kaum sab xis ntawm lub sab luj thiab lwm tus: A = (A-B) / cosα = C / sinα = H / sinα.

Txij li thaum lub Trapezoid nrog txoj cai ces kaum yog ib tug cov ntaub ntawv ntawm lub Trapezoid, lwm cov qauv uas txiav txim cov nuj nqis, yuav sib ntsib thiab lub.

Properties incircle

Yog hais tias tus mob yog hais tias nyob rau hauv ib lub Trapezoid inscribed vajvoog, ces koj yuav tau siv cov nram qab no cov khoom:

- tus nqi ntawm lub hauv paus yog lub sum ntawm lub sab;

- deb ntawm cov sab saum toj ntawm lub lub zoo mus rau lub ntsiab lus ntawm tangency ntawm lub inscribed vajvoog yog yeej ib txwm sib npaug zos;

- qhov siab ntawm lub Trapezoid yog sib npaug zos rau cov sab, perpendicular mus rau lub hauv paus, thiab yog sib npaug zos rau lub lub cheeb ntawm lub voj voog ;

- lub voj voog center yog tus taw tes uas tshuam bisectors ntawm cov ces kaum ;

- yog hais tias tus sab sab ntawm lub taw tes ntawm kev sib cuag yog muab faib ua lengths N thiab M, ces tus voos kheej-kheej ntawm lub vajvoog yog sib npaug zos rau cov square hauv paus ntawm qhov khoom ntawm cov feem;

- quadrangle tsim los ntawm cov ntsiab lus ntawm kev sib cuag, lub sab saum toj ntawm lub Trapezoid thiab qhov chaw ntawm lub inscribed vajvoog - nws yog ib tug square, nws sab yog sib npaug zos rau lub ib voos ncig;

- thaj tsam ntawm lub daim duab yog qhov khoom ntawm yog vim li cas thiab cov khoom ntawm ib nrab-sum ntawm bases nyob rau hauv nws qhov siab.

Zoo li trapeze

Cov npe no yog heev pab tau rau kev kawm cov thaj chaw ntawm geometric nuj nqis. Piv txwv li, lub kab pheeb ces kaum phua rau hauv cov plaub cov vajvoos peb sab Trapezoid, thiab yog nyob ib sab mus rau lub hauv paus ntawm cov zoo li, thiab mus rau lub sab - sib npaug zos. Qhov no daim ntawv qhia yuav hu ua ib tug ntawm cov vajvoos peb sab, uas yog tawg trapeze nws diagonals. Thawj feem ntawm tsab ntawv no yog muaj pov thawj los ntawm lub kos npe rau ntawm kev zoo sib thooj ntawm ob ces kaum. Los ua pov thawj rau hauv lub thib ob yog ib feem yog zoo dua siv tus qauv teev tseg hauv qab no.

lub pov thawj

Txais nyiaj uas ABSD (AD thiab BC - lub hauv paus ntawm lub Trapezoid) yog tawg diagonals HP thiab AC. Tus taw tes ntawm kev tshuam - O. Peb tau txais plaub cov vajvoos peb sab: AOC - nyob rau ntawm sab puag, Bos - lub sab sauv puag, ABO thiab sod nyob rau sab. Duab peb ceg sod thiab biofeedback muaj ib qho qhov siab nyob rau hauv cov ntaub ntawv uas, yog hais tias tus theem ntawm NPAWG thiab OD yog lawv bases. Peb nrhiav tau tias qhov txawv ntawm lawv cheeb tsam (P) sib npaug zos rau cov sib txawv ntawm cov feem: PBOS / PSOD = NPAWG / ML = K. Thiaj li, PSOD = PBOS / K. Ib yam li ntawd, lub duab peb ceg AOB thiab biofeedback muaj ib qho qhov siab. Txais rau lawv lub hauv paus feem SB thiab Oa. Peb tau PBOS / PAOB = CO / Oa = K thiab PAOB = PBOS / K. Los ntawm no nws raws li nram no uas PSOD = PAOB.

Yuav kom sau cov ntaub ntawv uas cov menyuam kawm ntawv xav kom nrhiav tau ib tug kev twb kev txuas ntawm lub qhov chaw ntawm cov vajvoos peb sab tau, uas yog tawg trapeze nws diagonals, txiav txim siab seb tom ntej no hauj lwm. Nws yog lub npe hu hais tias cov vajvoos peb sab Bos thiab ADP chaw yog muaj sib npaug, nws yog tsim nyog los nrhiav tau rau thaj tsam ntawm ib tug Trapezoid. Txij li thaum PSOD = PAOB, ces PABSD PBOS + = PAOD + 2 * PSOD. Los ntawm cov kev zoo sib thooj ntawm cov vajvoos peb sab Bos thiab ANM li nram no uas NPAWG / OD = √ (PBOS / PAOD). Thiaj li, PBOS / PSOD = NPAWG / OD = √ (PBOS / PAOD). Tau PSOD = √ (* PBOS PAOD). Ces PABSD PBOS + = PAOD + 2 * √ (PAOD PBOS *) = (+ √PBOS √PAOD) 2.

zog kev zoo sib thooj

Ntxiv rau tsim lub ntsiab lus no, nws yog ua tau los ua pov thawj, thiab lwm yam ntxwv ntawm lub trapezoids. Yog li ntawd, nrog rau cov kev pab los ntawm kev zoo sib thooj yuav ua pov thawj cov cuab yeej ya, uas kis los ntawm tus taw tes tsim los ntawm cov kev tshuam ntawm lub diagonals ntawm lub geometric duab, thaum uas tig mus rau hauv av. Rau no peb yuav daws tau qhov nram qab no teeb meem: nws yog tsim nyog los nrhiav tau qhov ntev RK ya uas kis los ntawm tus taw tes O. Los ntawm cov kev zoo sib thooj ntawm cov vajvoos peb sab ADP thiab SPU li nram no tias cov AO / OS = AD / BS. Los ntawm cov kev zoo sib thooj ntawm cov vajvoos peb sab ADP thiab ASB li nram no uas AB / AC = PO / AD = BS / (BP + BS). Qhov no paub licas hais tias cov BS * PO = AD / (AD + BC). Ib yam li ntawd, los ntawm kev zoo sib thooj ntawm cov vajvoos peb sab MLC thiab ABR li nram no uas OK * BP = BS / (BP + BS). Qhov no paub licas hais tias cov OC thiab RC = RC = 2 * BS * AD / (AD + BC). Ya dua los ntawm cov kev tshuam taw tes ntawm cov diagonals thaum uas tig mus rau lub hauv paus thiab txuas ob sab, cov kev tshuam taw tes yog phua rau hauv ib nrab. Nws ntev - yog lub harmonic phem ntawm yog vim li cas cov nuj nqis.

Xav txog cov nram qab no cov yam ntxwv ntawm ib tug Trapezoid, uas yog hu ua cov cuab yeej ntawm plaub cov ntsiab lus. lub point ntawm kev tshuam ntawm lub diagonals (D), cov kev tshuam ntawm lub txuas ntxiv rau sab (E) raws li mid-bases (T thiab G) yeej ib txwm dag nyob rau tib kab. Nws yog ib qho yooj yim los ua pov thawj kev zoo sib thooj txoj kev. Cov uas ua cov vajvoos peb sab yog zoo xws li cov bes thiab AED, thiab txhua tus xws li ib tug nruab nrab ET thiab DLY faib lub apex lub E nyob rau hauv sib npaug zos qhov chaw. Li no, taw tes E, T thiab F yog collinear. Ib yam li ntawd, nyob rau hauv tib yam kab yog cov txheej txheem ntawm nyob rau hauv cov nqe lus ntawm T, O, thiab G. no raws li nram no los ntawm kev zoo sib thooj ntawm cov vajvoos peb sab Bos thiab ANM. Li no peb xaus uas tag nrho plaub nqe lus - E, T, O thiab F - yuav dag rau ib tug ncaj kab.

Siv zoo xws li cov trapezoids, yuav tsum muab rau cov menyuam kawm ntawv nrhiav tau qhov ntev ntawm lub ya (LF), uas cais lub daim duab mus rau hauv ob zoo li. Qhov kev txiav no yuav tsum yog thaum uas tig mus rau lub bases. Txij li thaum tus tau txais Trapezoid ALFD LBSF thiab zoo sib xws, cov BS / LF = LF / AD. Qhov no implies tias LF = √ (BS * BP). Peb xaus hais tias cov ya uas faib mus rau hauv ob trapezium li, muaj ib tug ntev sib npaug zos rau cov geometric phem ntawm lub lengths ntawm cov kev bases xam.

Xav txog cov nram qab no zoo sib thooj cov cuab yeej. Nws yog raws li nyob rau hauv lub ya uas faib lub Trapezoid rau hauv ob sib npaug zos loj daim. Txais hais tias trapeze ABSD ya yog muab faib ua ob zoo xws li cov EH. Los ntawm cov saum toj kawg nkaus ntawm B nws txo qis rau qhov siab ntawm uas ya yog muab faib ua ob qhov chaw EN - B1 thiab B2. Muab PABSD / 2 = (BS + EH) * V1 / 2 = (AP + EH) * B2 / 2 = PABSD (BP + BS) * (B1 + B2) / 2. Ntxiv compose lub system, nyob rau lub thawj kab zauv (BS + EH) * B1 = (BP + EH) * B2 thiab thib ob (BS + EH) * B1 = (BP + BS) * (B1 + B2) / 2. Nws hais ntxiv hais tias B2 / B1 = (BS + EH) / (BP + EH) thiab BS + EH = ((BS + BP) / 2) * (1 + B2 / B1). Peb pom tau hais tias qhov ntev ntawm faib lub Trapezoid nyob rau hauv ob sib npaug zos, sib npaug zos rau hauv nruab nrab lengths ntawm lub quadratic bases: √ ((CN2 + aq2) / 2).

kev zoo sib thooj cov lus xaus

Yog li, peb tau muaj pov thawj tias:

1. Tus ya txuas rau hauv nruab nrab ntawm lub Trapezoid nyob rau sab sab, thaum uas tig mus BP thiab BS thiab BS yog lub xam txhais li cas thiab BP (puag ntev ntawm ib tug Trapezoid).

2. Tus bar dua los ntawm tus taw tes O ntawm kev tshuam ntawm lub diagonals thaum uas tig mus AD thiab BC yuav sib npaug zos rau cov harmonic phem tooj BP thiab BS (2 * BS * AD / (AD + BC)).

3. Tus ya tawg nyob rau hauv uas zoo sib xws Trapezoid muaj ib tug ntev geometric phem bases BS thiab BP.

4. Lub caij uas faib lub zoo mus rau hauv ob sib npaug zos loj, ib tug ntev tau txhais hais tias square tooj BP thiab BS.

Yuav kom sau cov khoom thiab khiav ntawm linkages ntawm cov theem ntawm tus menyuam kawm ntawv yog tsim nyog los tsim lawv rau cov kev Trapezoid. Nws yuav yooj yim tso saib qhov nruab nrab txoj kab thiab lub ya uas kis los ntawm tus taw tes - cov kev tshuam ntawm lub diagonals ntawm cov nuj nqis - thaum uas tig mus rau hauv pem teb. Tab sis qhov twg yuav tsum yog tus thib peb thiab thib plaub? Qhov no teb yuav ua tus menyuam kawm ntawv mus rau lub foundations ntawm cov tsis paub hais tias kev sib raug zoo ntawm qhov nruab nrab qhov tseem ceeb.

Ya pub ntxiv tshaj qhov midpoints ntawm lub diagonals ntawm lub Trapezoid

Xav txog cov nram qab no khoom teejtug uas yog hauv daim duab. Peb tau lees tias cov ya MN yog thaum uas tig mus rau lub bases thiab faib nyob rau hauv ib nrab diagonally. lub point ntawm kev tshuam yog hu ua tus W thiab S. no ya yuav ua ncaj rau ib nrab ntawm cov sib txawv yog vim li cas. Cia peb kawm no nyob rau hauv ntau yam. MSH - qhov nruab nrab txoj kab ntawm daim duab peb sab ABS, nws yog sib npaug zos rau cov BS / 2. Minigap - nruab nrab txoj kab ntawm daim duab peb sab DBA, nws yog sib npaug zos rau AD / 2. Tom qab ntawd peb pom tau hais tias SHSCH = minigap-MSH yog li ntawd SHSCH = AD / 2-BS / 2 = (AD + BC) / 2.

center ntawm lub ntiajteb txawj nqus

Cia saib yuav ua li cas txhais tau lub caij rau ib tug muab geometrical daim duab. Ua li no, koj yuav tsum cuag puag hauv opposite lus qhia. Ua li cas nws txhais li cas? Nws yog tsim nyog los ntxiv rau lub hauv paus mus rau lub sab sauv hauv qab - mus tej yam ob tog, piv txwv li, mus rau sab xis. Ib tug qis cas sim haum qhov ntev ntawm lub Upper rau sab laug. Tom ntej no, txuas rau lawv kab pheeb ces kaum. Tus taw tes ntawm kev tshuam ntawm no ya nrog qhov chaw kab ntawm daim duab yog qhov chaw ntawm lub ntiajteb txawj nqus ntawm lub trapezium.

Inscribed thiab piav trapeze

Wb daim ntawv teev nta xws nuj nqis:

1. Kab yuav inscribed nyob rau hauv ib lub voj voog xwb yog hais tias nws yog ceskaum.

2. Nyob ib ncig ntawm lub voj voog yuav piav raws li ib tug Trapezoid, muab hais tias lub sum ntawm cov lengths ntawm lawv bases yog lub sum ntawm cov lengths ntawm lub sab.

Qhov yuav tshwm ntawm lub inscribed vajvoog:

1. Lub qhov siab ntawm cov Trapezoid piav ib txwm sib npaug zos rau ob zaug lub voos kheej-kheej.

2. Cov sab ntawm lub Trapezoid piav saib los ntawm qhov chaw ntawm lub vajvoog ntawm txoj cai ces kaum.

Tus thawj tsim nyog tau yog cuab kev, thiab ua pov thawj rau ob yog yuav tsum tau mus nrhiav kom tau hais tias lub kaum sab xis ntawm sod yog ncaj qha, uas yog, nyob rau hauv qhov tseeb, kuj tsis yooj yim. Tab sis qhov kev paub ntawm cov cuab yeej no tso cai rau koj siv ib txoj cai daim duab peb sab los daws teeb meem.

Tam sim no peb qhia kom meej rau txim rau lub ceskaum Trapezoid, uas yog inscribed nyob rau hauv ib lub voj voog. Peb tau hais tias tus siab yog lub geometric mean daim duab bases: H = 2R = √ (BS * BP). Kom muaj raws li qhov yooj yim txoj kev ntawm kev daws teeb meem rau cov trapezoids (lub hauv paus ntsiab lus ntawm ob heights), cov tub ntxhais kawm ntawv yuav tsum daws tau qhov nram qab no ua hauj lwm. Txais hais tias BT - rau qhov siab ntawm lub ceskaum nuj nqis ABSD. Koj yuav tau mus nrhiav stretches ntawm AT thiab AP. Thov cov mis piav saum toj no, nws yuav ua li cas yog tsis yog yooj yim.

Tam sim no cia peb piav qhia txog yuav ua li cas los mus txiav txim lub voos kheej-kheej ntawm lub vajvoog los ntawm cov cheeb tsam piav Trapezoid. Rho los ntawm cov saum toj kawg nkaus B siab rau puag BP. Txij li thaum lub vajvoog inscribed nyob rau hauv lub Trapezoid, lub BS + 2AB = BP los yog AB = (BS + BP) / 2. Los ntawm daim duab peb sab ABN xyuas sinα = BN / 2 * AB = BN / (AD + BC). PABSD = (BS + BP) BN * / 2, BN = 2R. Muab PABSD = (BP + BS) * R, nws hais ntxiv hais tias R = PABSD / (AD + BC).

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Tag nrho cov qauv midline trapeze

Tam sim no nws yog lub sij hawm mus kom kawg yam khoom ntawm no geometric duab. Peb yuav to taub, dab tsi yog qhov nruab nrab txoj kab ntawm lub Trapezoid (M):

1. Los ntawm bases: M = (A + B) / 2.

2. Tom qab lub qhov siab, lub hauv paus thiab cov ces kaum:

• M-H = A * (ctgα + ctgβ) / 2;

• M + H = D * (ctgα + ctgβ) / 2.

3. Los ntawm ib qhov siab thiab kab pheeb ces kaum lub therebetween. Piv txwv li, D1 thiab D2 - kab pheeb ces kaum ntawm lub trapezium; α, β - lub kaum sab xis ntawm lawv:

M = D1 * D2 * sinα / 2 H = D1 * D2 * sinβ / 2H.

4. Nyob rau hauv lub cheeb tsam thiab qhov siab: M = R / N.