Opendekera equilateral trapezoid. Kodi mzere pakati pa trapezoid ndi. Mitundu ya trapezoids. Oimba ng'oma pamodzi - izo ..

Oimba ng'oma pamodzi - wapadera nkhani ya quadrangle, pamene peyala imodzi ya mbali likufanana. Mawu akuti "trapezoid" anachokera ku mawu achigiriki τράπεζα, kutanthauza "tebulo", "tebulo". M'nkhaniyi tiona mitundu ya oimba ng'oma pamodzi ndi katundu wake. Komanso, tidzamva mmene kuwerengera zinthu payekha mwa chithunzi geometrical. Mwachitsanzo, opendekera ya trapezium equilateral, pakati mzere, m'dera ndi ena. Mabukuwa ali ndi maziko masamu wotchuka kalembedwe, T. E. Mwa njira mosavuta.

mwachidule

Choyamba, tiyeni kumvetsa zomwe quadrangle. chiwerengerochi ndi nkhani yapadera ya polygon ndi mbali zinayi ndi mfundo zinayi. Awiri mfundo za quadrilateral ndi zimene sizili pafupi, wotchedwa zosiyana. N'chimodzimodzinso anati kwa ziwiri mbali sanali pafupi. The mitundu ikuluikulu ya quadrangles - ndi parallelogram, rectangle, rhombus, lalikulu, trapezoid ndi deltoid.

Choncho kuti oimba ng'oma pamodzi ndi. Monga tanena kale, chithunzi ichi mbali ziwiri ndi kufanana. Iwo akutchedwa zapansi. Ena awiri (sanali kufanana) - mbali. Zipangizo za mayeso osiyanasiyana mayeso zambiri mukhoza kukumana ndi mavuto kugwirizana ndi trapezoids amene njira amafunika kudziwa wophunzira si ataphimbidwa ndi pulogalamu. Sukulu Masamu anayambitsanso ana ndi kumathandiza kupeza ngodya zabwino katundu ndi diagonals komanso mzere apakatikati a trapezoid isosceles. Koma ena kuposa onena za mawonekedwe zojambula lili ndi zinthu zina. Koma iwo pambuyo ...

mitundu oimba ng'oma pamodzi

Pali mitundu yambiri ya chithunzi ichi. Komabe nthawi zambiri mwambo kuganizira awiriwo - isosceles ndi anayi.

1. amakona anayi trapezoid - chithunzi imene a m'mbali perpendicular maziko a. Iye ali kumathandiza kupeza ngodya ziwiri nthawi zonse wofanana madigiri nainte.

2. isosceles trapezium - ndi zojambula chithunzi amene adzamenyane ndi ofanana. Choncho, ndi kumathandiza kupeza ngodya zabwino pa tsinde komanso ali ofanana.

Mfundo zikuluzikulu za njira kuphunzira katundu wa trapezoid ndi

The mfundo monga kugwiritsa ntchito otchedwa ntchito njira. Ndipotu, palibe kulowa ongolankhula Inde Masamu katundu watsopano chithunzi ichi. Iwo akhoza kukhala womasuka kapena m'kati popanga ntchito zosiyanasiyana (dongosolo bwino). Nkofunika kuti mphunzitsi kudziwa zimene nonse muyenera kuika patsogolo pa ophunzira pa nthawi iliyonse ya kuphunzira. Komanso, aliyense katundu trapezoid akhoza ankayimiridwa ngati ntchito zenizeni mu dongosolo ntchito.

Mfundo yachiwiri ndi otchedwa mwauzimu gulu la kafukufuku "chidwi" oimba ng'oma pamodzi ndi katundu. Izi zikutanthauza kuti anthu ndondomeko ya kuphunzira zinthu payekha chithunzi zojambula. Motero, ophunzira mosavuta kuwakumbukira. Mwachitsanzo, chuma cha mfundo zinayi. Iwo akhoza kukhala ndi umboni monga mwa kuphunzira kufanana ndipo kenako ntchito zamoyo zina. A Triangles Wofanana pafupi m'mbali mwa zimakwana, n'zotheka kutsimikizira ndi ntchito osati katundu wa Triangles ndi misanje ofanana imachitika m'mbali umene kugona pa mzere molunjika, komanso pogwiritsa ntchito chilinganizo S = 1/2 (AB * sinα). Komanso, n'zotheka ntchito lamulo la sines kwa trapezium alembedwa kapena-angled makona ndi trapezoid anafotokoza mu T. D.

Ntchito "linalake ku" zimaonetsa zojambula chithunzi mu zili kumene sukulu - ndi tasking chiphunzitso chawo luso. Zonse Buku kuphunzira katundu wa ndimeyi wa ena amalola ophunzira kuphunzira oimba ng'oma pamodzi mwakuya ndi zipangitsa bwino ntchitoyo. Kotero, ife chitani kuphunzira chithunzi ameneyu.

Zochitika ndi katundu wa trapezoid isosceles

Monga taonera, mu chithunzi ichi zojambula mbali ofanana. Koma amadziwika monga trapezoid bwino. Ndipo kodi izo chidwi chake nalo dzina lake? Mbali yapadera ya chithunzi ichi anafotokoza kuti iye ali ndi mbali ofanana ndi kumathandiza kupeza ngodya zabwino pa tsinde, komanso diagonally. Komanso, Uwerenge kumathandiza kupeza ngodya zabwino za trapezoid isosceles ndi wofanana ndi madigiri 360. Koma si onse! mozungulira Only isosceles tinganene kuti ndi lozungulira trapezoids onse odziwika. Ichi ndi chifukwa chakuti Uwerenge kumathandiza kupeza ngodya zabwino ufalikire chithunzi ichi ndi madigiri 180, ndipo kokha pansi pa chikhalidwe izi zikhoza kukhala mozungulila quadrangle anafotokoza. The katundu zotsatirazi chithunzi zojambula ndi mtunda kuchokera pamwamba pa m'munsi kwa ziyerekezo nsonga otsutsana pa mzere kuti lili m'munsi uyu adzakhala wofanana midline lapansi.

Tsopano tiyeni tione mmene kupeza ngodya ya trapezoid isosceles. Taonani yankho pabvuto ili, malinga ndi kukula kwa zipani kudziwika chithunzi.

chisankho

Adafuna potanthauza quadrangle makalata A, B, C, D, kumene BS ndi BP - maziko. Mu trapezoid isosceles mbali ofanana. Tingayerekezere kuti kukula ndi wofanana ndi X ndi Y miyeso ndi zapansi ndi Z (wamng'ono ndi wamkulu, motero). Pakuti mawerengedwe a mbali ya kufunika pochita kutalika H. Chifukwa ndi bwino-angled makona ABN kumene AB - ndi hypotenuse, ndi BN ndi AN - miyendo. Kuwerengetsa kukula kwa mwendo AN: kuchotsera kwa m'munsi zikuluzikulu kochepa, ndipo zotsatira lagawidwa ndi 2. lemba chilinganizo: (ZY) / 2 = F. Tsopano, kuwerengetsa ngodya pachimake cha makona ntchito ntchito Ko. Timapeza kulowa zotsatirazi: Ko (β) = X / F. Tsopano kuwerengera ngodya: β = arcos (X / F). Komanso, podziwa kona tingadziwire ndipo chachiwiri, kupanga maziko masamu ntchito: 180 - β. kumathandiza kupeza ngodya zabwino anafotokozedwa.

Palinso njira yachiwiri vutoli. Pachiyambi mulibe ngodya mu msinkhu wa mwendo N. linaŵerengera mtengo wa BN. Tikudziwa kuti lalikulu la hypotenuse wa kansalu bwino ndi wofanana Uwerenge mabwalo mbali zina ziwiri. Ife tifika: BN = √ (X2 F2). Kenako, tigwiritsa ntchito trigonometric ntchito tg. Chotsatira: β = arctg (BN / F). Ngodya pachimake wapezeka. Kenako, tingamasulire makona obtuse monga njira zoyambirira.

Cholowa cha diagonals ya trapezoid isosceles

Choyamba, ife kulemba malamulo anayi. Ngati opendekera mu trapezoid isosceles ndi perpendicular, ndiye:

- kutalika kwa chithunzi ndi wofanana Uwerenge zapansi, anagawa ndi awiri;

- kutalika kwake ndi mzere pakati zimakhala zofanana;

- dera trapezoid ndi chofanana ndi lalikulu la kumwamba (pakati mzere kuti zapansi theka);

- lalikulu la opendekera a lalikulu ndi wofanana ndi ndalama theka la kawiri zapansi lalikulu kapena midline (kutalika).

Tsopano yang'anani pa njira kumasulira opendekera ndi trapezoid equilateral. chidutswa cha mudziwe akhoza kugawidwa m'magulu anayi:

1. chilinganizo opendekera kutalika kudzera mbali.

Tingayerekezere kuti ndi - m'munsi m'munsi, B - Top, C - mbali ofanana, D - opendekera. Pankhaniyi, kutalika zingadziŵike motere:

D = √ (C 2 + A * B).

2. chilinganizo cha kutalika opendekera wa cosine lapansi.

Tingayerekezere kuti ndi - m'munsi m'munsi, B - Top, C - mbali ofanana, D - opendekera, α (m'munsi m'munsi) ndi β (chapamwamba m'munsi) - ngodya trapezoid. Timapeza chilinganizo zotsatirazi, ndi amene angathe kuwerengetsa zaka za opendekera:

- 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. chilinganizo opendekera kutalika ndi trapezoid isosceles.

Tingayerekezere kuti ndi - m'munsi m'munsi, B - chapamwamba, D - opendekera, M - mzere pakati H - kutalika, P - Malo trapezoid, α ndi β - ngodya pakati diagonals. Kudziwa kutalika kwa mitunduyi zotsatirazi:

- D = √ (m2 + N2);

- D = √ (H 2 + (A + B) 2/4);

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

Pakuti Pankhaniyi, chilingano: sinα = sinβ.

4. chilinganizo opendekera m'litali mwa mumbali ndi kutalika.

Tingayerekezere kuti ndi - m'munsi m'munsi, B - Top, C - mbali, D - opendekera, H - kutalika, α - ngodya ndi maziko m'munsi.

Kudziwa kutalika kwa mitunduyi zotsatirazi:

- D = √ (H 2 + (A-P * ctgα) 2);

- D = √ (H 2 + (B + F * ctgα) 2);

- D = √ (A2 + S2-2A * √ (C2-H2)).

Zochitika ndi katundu wa trapezium amakona anayi

Tiyeni tione kodi chidwi chithunzi ichi geometrical. Monga tanena kale, tili ndi amakona anayi trapezoid kumathandiza kupeza ngodya ziwiri bwino.

Kuwonjezera pa tanthauzo chakale, pali ena. Mwachitsanzo, amakona anayi trapezoid - ndi trapezoid imene mbali imodzi ndi perpendicular maziko a. Kapena kuwumba ndi pa kumathandiza kupeza ngodya zabwino mbali. Mu mtundu uwu wa trapezoids kutalika ndi mbali kuti ndi perpendicular kwa zapansi lapansi. Pakati mzere - ndi gawo limene limalumikizana ndi midpoints wa mbali ziwiri. Chuma cha mchitidwe anati ndi kuti likufanana ndi zapansi ndi wofanana ndi theka la ndalama zawo.

Tsopano tiyeni tikambirane mitunduyi zikuluzikulu zomwe chimatanthauza akalumikidzidwa zojambula. Kuti tichite zimenezi, tiyenera kuganiza kuti A ndi B - m'munsi; C (perpendicular kwa m'munsi) ndi D - mbali ya trapezium amakona anayi, M - mzere pakati, α - pachimake njingayo, P - m'deralo.

1. mbali perpendicular kwa zapansi, ndi chithunzi wolingana ndi kutalika (C = N), ndipo liri kutalika kwa wachiwiri mbali A ndi sine wa α mbali pa maziko wamkulu (C = A * sinα). Komanso, wofanana ndi mankhwala a tangent wa α pachimake ngodya ndi kusiyana zapansi: C = (A-B) * tgα.

2. Mbali D (osati perpendicular maziko a) wofanana ndi quotient za kusiyana kwa A ndi B ndipo cosine (α) kapena ngodya pachimake kwa kutalika payekha anaŵerengera H ndi sine pachimake ngodya: A = (A-B) / Ko α = C / sinα.

3. Mbali kuti ndi perpendicular kwa zapansi, ndi wofanana ndi muzu lalikulu la m'bwalo la kusiyana D - mbali yachiwiri - ndi kusiyana lalikulu m'munsi:

C = √ (q2 (A-B) 2).

4. Mbali A trapezoid amakona anayi ndi wofanana ndi muzu lalikulu la ndalama lalikulu la mbali lalikulu ndi C zapansi zojambula mawonekedwe kusiyana: D = √ (C 2 + (A-B) 2).

5. mbali C ndi wofanana ndi quotient wa lalikulu awiri Uwerenge zapansi ake: C = P / M = 2P / (A + B).

6. m'dera chimafotokozera mankhwala M (pakati mzere wa trapezoid amakona anayi) kutalika kapena malangizo lateral perpendicular kwa zapansi: P = M * N = M * C.

7. Udindo C ndi quotient wa kawiri mawonekedwe lalikulu ndi mankhwala sine pachimake ngodya ndi Uwerenge zapansi ake: C = P / M * sinα = 2P / ((A + B) * sinα).

8. mbali chilinganizo cha trapezium amakona anayi kudzera opendekera ake, ndi ngodya pakati pawo:

- sinα = sinβ;

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

kumene D1 ndi D2 - opendekera wa trapezoid ndi; α ndi β - ngodya pakati pawo.

9. chilinganizo mbali mwa ngodya m'munsi m'munsi ndi ena: A = (A-B) / cosα = C / sinα = H / sinα.

Popeza trapezoid ndi kumathandiza kupeza ngodya zabwino bwino ndi makamaka nkhani ya trapezoid, ndi mitunduyi ena kuti adziwe Chiwerengerochi, adzakomana ndi anayi.

katundu incircle

Ngati chikhalidwe Akuti mu amakona anayi trapezoid alembedwa bwalo, ndiye inu mukhoza kugwiritsa ntchito katundu zotsatirazi:

- kuchuluka kwa m'munsi ndi Uwerenge mbali;

- mtunda kuchokera pamwamba pa amakona anayi mawonekedwe ndi mfundo za tangency mwa bwalo alembedwa nthawi zonse ndi zofanana;

- kutalika kwa trapezoid ndi wofanana mbali, perpendicular kwa zapansi, ndipo ndi ofanana ndi m'mimba mwake mwa bwalo ;

- pakati bwalo ndi mfundo zomwe intersect bisectors wa kumathandiza kupeza ngodya zabwino ;

- ngati mbali lateral wa mfundo zokhudzana lagawidwa amayesetsa N ndi M, ndiye utali wozungulira bwalo ndi wofanana ndi muzu lalikulu chipatso cha zigawo izi;

- quadrangle popangidwa ndi mfundo za kukhudzana, pamwamba pa trapezoid ndi likulu la bwalo alembedwa - ndi lalikulu, kumbali ndiyofanana ndi utali wozungulira ndi;

- dera chithunzi ndi mankhwala chifukwa ndi mankhwala a theka Uwerenge zapansi pa msinkhu wake.

Similar oimba ng'oma pamodzi

Nkhani imeneyi ndi zothandiza kwambiri chifukwa chophunzira katundu wa kanjedza zojambula. Mwachitsanzo, kugawanika opendekera mu Triangles anayi trapezoid, ndipo pafupi m'munsi mwa monga, ndi mbali - a ofanana. mawu awa angatchedwe chuma cha Triangles, umene uli wosweka ndi oimba ng'oma pamodzi diagonals ake. Gawo loyamba la mawu amenewa imatsimikizirika kudzera chizindikiro cha kufanana kwa ngodya ziwiri. Pofuna kutsimikizira gawo lachiwiri ndi bwino kugwiritsa ntchito njira zimene zili pansipa.

chitsimikizo

Kuvomereza kuti chithunzi ABSD (AD ndi BC - maziko a trapezoid ndi) wathyoka diagonals HP ndi AC. Mfundo ya mphambano - O. Ife tifika Triangles zinayi: AOC - m'munsi m'munsi, Bos - m'munsi chapamwamba, ABO ndi SOD mumbali. Triangles SOD ndi biofeedback ndi kutalika wamba mu choncho, ngati zigawo za Bo ndi od ndi zapansi awo. Ife tikupeza kuti kusiyana kwa madera awo (P) wofanana ndi kusiyana kwa zigawo izi: PBOS / PSOD = Bo / ml = K. Choncho, PSOD = PBOS / K. Mofananamo, Triangles AOB ndi biofeedback ndi kutalika wamba. Amavomerezedwa zigawo zawo m'munsi SB ndipo o. Timapeza PBOS / PAOB = NKHA / o = K ndi PAOB = PBOS / K. Kuchokera pamenepa, ndizoonekeratu kuti PSOD = PAOB.

Kulimbitsa ophunzira zinthu akulimbikitsidwa kupeza kugwirizana pakati pa mbali ya Triangles analandira umene uli wosweka ndi oimba ng'oma pamodzi diagonals ake, poganizira za ntchito yotsatira. Amadziwika kuti Triangles Bos ndi ADP malo ofanana, m'pofunika kupeza dera trapezoid ndi. Popeza PSOD = PAOB, ndiye PABSD PBOS + = PAOD + 2 * PSOD. Kuyambira kufanana kwa Triangles Bos ndi ANM motere kuti Bo / od = √ (PBOS / PAOD). Choncho, PBOS / PSOD = Bo / od = √ (PBOS / PAOD). Pezani PSOD = √ (* PBOS PAOD). Ndiye PABSD PBOS + = PAOD + 2 * √ (PAOD PBOS *) = (+ √PBOS √PAOD) 2.

katundu kufanana

Kupitiriza kukhala mutu uwu, n'zotheka kuti atsimikizire, ndi mbali zina zosangalatsa za trapezoids lapansi. Choncho, mothandizidwa ndi kufanana akhoza kutsimikizira gawo katundu wakupambana mwa mfundo aumbike mwa mphambano ya diagonals wa chithunzi zojambula, ikufanana pansi. Pakuti ichi tinena vuto zotsatirazi: m'pofunika kupeza kutalika RK gawo kuti umadutsa mpaka O. Kuchokera kufanana kwa Triangles ADP ndi SPU motere kuti AO / Os = AD / BS. Kuyambira kufanana kwa Triangles ADP ndi ASB motere kuti AB / AC = PO / AD = BS / (BP + BS). Izi zikutanthauza kuti BS ya * PO = AD / (AD + BC). Mofananamo, kuchokera kufanana kwa Triangles MLC ndi ABR motere kuti Chabwino * BP = BS / (BP + BS). Izi zikutanthauza kuti OC ndi RC = RC = 2 * BS * AD / (AD + BC). Gawo kudutsa mphambano mfundo za diagonals kufanana kwa m'munsi ndi kulumikiza mbali ziwiri, mphambano mfundo ng'ambidwa pakati. M'litali - ndi zikutanthauza amgwirizano wa kanjedza chifukwa.

Taganizirani makhalidwe awa a trapezoid ndi wotchedwa chuma cha mfundo zinayi. kufika mphambano ya diagonals ndi (D), ndi mphambano ya kupitiriza mbali (E) komanso m'ma zapansi (T ndi G) nthawi zonse kunama pa mzere womwewo. N'zosavuta kutsimikizira njira kufanana. The Triangles chifukwa ofanana BES ndi AED, ndipo aliyense kuphatikizapo apakatikati opuma ndipo DLY kugawa pamwamba ngodya E m'madera ofanana. Choncho, mfundo E, T ndi F ndi collinear. Mofananamo, pa mzere womwewo imakonzedwa mu mawu a T, O, ndi G. Izi motere kuchokera kufanana kwa Triangles Bos ndi ANM. Choncho tinganene kuti mawu onse anayi - E, T, O ndi F - adzagona pa mzere wolunjika.

Kugwiritsa trapezoids zofanana, adzapelekedwa ophunzira kupeza kutalika kwa gawo (LF), lomwe limapanga malire zimakwana m'magulu awiri ngati. odulidwa Izi ziyenera kufanana ndi zapansi ndi. Popeza analandira trapezoid ALFD LBSF ndi yofanana, BS / LF = LF / AD. Izi zikutanthauza kuti LF = √ (BS * BP). Tinganene kuti gawo kuti ukugawa mu awiri trapezium ngati, ali kutalika wofanana ndi zikutanthauza zojambula za utali wa zapansi ndi kuzilingalira.

Taganizirani izi chuma kufanana. Bukuli lili ndi gawo limene ukugawa trapezoid zidutswa ziwiri wofanana kukula. Kuvomereza kuti gawo oimba ng'oma pamodzi ABSD lagawidwa awiri ofanana ee. Kuchokera pamwamba pa B adatchithisira pamwamba pa gawo kuti lagawidwa pawiri EN - B1 ndi B2. Kupeza PABSD / 2 = (BS + ee) * V1 / 2 = (AP + ee) * B2 / 2 = PABSD (BP + BS) * (B1 + B2) / 2. Komanso kulemba dongosolo, mmene anthu aone kuti pali choyamba (BS + ee) * B1 = (BP + ee) * B2 ndi wachiwiri (BS + ee) * B1 = (BP + BS) * (B1 + B2) / 2. Tidziwanso kuti B2 / B1 = (BS + EN) / (BP + EN) ndi BS EN + = ((BS + BP) / 2) * (1 + B2 / B1). Ife tikupeza kuti kutalika kugawa trapezoid awiri ofanana, wofanana ndi zotalika pafupifupi ya zapansi ndi quadratic: √ ((CN2 + aq2) / 2).

kufanana mfundo

Choncho, ife asonyeza kuti:

1. gawo kulumikiza pakati pa trapezoid pa mbali lateral, ikufanana ndi BP ndi BS ndi BS ndi masamu zikutanthauza ndi (kutalika m'munsi mwa trapezoid a) BP.

2. bala kudutsa mpaka O a mphambano ya diagonals kufanana AD ndi BC adzakhala wofanana ndi amgwirizano manambala zikutanthauza BP ndi BS (2 * BS * AD / (AD + BC)).

3. The gawo kuswa mu trapezoid ofanana ali kutalika zojambula zikutanthauza zapansi BS ndi BP.

4. mfundo ukugawa mawonekedwe mu awiri kukula wofanana, kutalika ndi zikutanthauza manambala apakati BP ndi BS.

Kulimbitsa zakuthupi ndi kuzindikira kulumikizana pakati pa zigawo za wophunzira m'pofunika kuti alimbikitsidwe kuti trapezoid yeniyeni. N'zosavuta kusonyeza mzere pafupifupi ndi gawo kuti umadutsa mfundo - ndi mphambano ya diagonals a manambalawo - kufanana pansi. Koma kodi kukhala lachitatu ndi lachinayi? Zimenezi zidzapangitsa wophunzirayo atulukira ubwenzi zosadziwika pakati pa mfundo pafupifupi.

Gawo kugwirizana midpoints wa diagonals wa trapezoid ndi

Taganizirani chuma zotsatirazi maonekedwe. Timavomereza kuti gawo MN likufanana ndi zapansi ndi kugawa mu theka diagonally. kufika mphambano amatchedwa W ndi S. gawo Izi kukhala wolingana ndi theka chifukwa kusiyana. Tiyeni tione izi mwatsatanetsatane. MSH - mzere pafupifupi ya makona ABS, ndi wofanana ndi BS / 2. Minigap - mzere pakati pa makona mosavemerezeka, ndi wofanana AD / 2. Ndiye ife tikupeza kuti SHSCH = minigap-MSH Choncho SHSCH = AD / 2-BS / 2 = (AD + BC) / 2.

pakati yokoka

Tiyeni tione mmene kufotokoza zinthu chifukwa anapatsidwa chithunzi geometrical. Kuti tichite zimenezi, muyenera kuwonjezera m'munsi mbali zosiyana. Kodi zikutanthauza chiyani? M'pofunika kuwonjezera m'munsi pansi chapamwamba - aliyense wa zipani Mwachitsanzo, kumanja. A m'munsi kupitiriza kutalika kumanzere chapamwamba. Kenako, kulumikiza opendekera awo. Mfundo ya mphambano za gawo ili ndi malo mzere wa chithunzi ndi likulu la kufunika kwa trapezium lapansi.

Lolembedwa ndi anafotokoza oimba ng'oma pamodzi

Tiyeni mndandanda zimaonetsa kanjedza amenewa:

1. Line akhoza alembedwa bwalo kokha ngati isosceles.

2. Kuzungulira bwalo akhoza monga trapezoid wina, malinga Uwerenge zotalika zapansi awo ndi Uwerenge zotalika mbali.

Zotsatira za bwalo lolembedwa:

1. Kutalika kwa trapezoid anafotokoza zonse wofanana kawiri utali wozungulira wa.

2. mbali ya trapezoid anafotokoza amakuona kuchokera pakati pa bwalo pa kumathandiza kupeza ngodya zabwino bwino.

Chotsatira woyamba ndi zoonekeratu, ndi kutsimikizira chachiwiri chofunika kutsimikizira kuti mbali ya SOD ndi mwachindunji, kuti Ndipotu, komanso si kophweka. Koma chidziwitso cha chuma ichi limakupatsani ntchito kansalu yabwino yothetsera mavuto.

Tsopano ife mwachindunji zotsatira za trapezoid isosceles, lomwe linalembedwa mu bwalo. Timapeza kuti kutalika ndi zojambula zikutanthauza chithunzi zapansi: H = 2R = √ (BS * BP). Kukwaniritsa njira zoyambirira za kuthetsa mavuto trapezoids (mfundo ya pamwamba awiri), wophunzira ayenera kuthetsa ntchito zotsatirazi. Kuvomereza kuti BT - kutalika kwa isosceles ziwerengero ABSD. Muyenera kupeza akutambasula wa AT ndi AP. Kugwiritsa ntchito mfundo zimene tafotokozazi, udzachite sikovuta.

Tsopano tiyeni tione mmene kudziwa utali wozungulira bwalo m'dera anafotokoza trapezoid. Mulibe pamwamba B kutalika pa BP m'munsi. Popeza bwalo alembedwa trapezoid, ndi BS + 2AB = BP kapena AB = (BS + BP) / 2. Kuchokera makona ABN anapezazo sinα = BN / 2 * AB = BN / (AD + BC). PABSD = (BS + BP) BN * / 2, BN = 2R. Kupeza PABSD = (BP + BS) * R, ndizoonekeratu kuti R = PABSD / (AD + BC).

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Njira zonse midline oimba ng'oma pamodzi

Tsopano ndi nthawi yoti mupite katunduyo lotsiriza la chithunzi ichi zojambula. Ife adzamvetsa, kodi mzere pakati pa trapezoid (M):

1. Kupyolera zapansi: M = (A + B) / 2.

2. Pambuyo kutalika, m'munsi ndi ngodya:

• M-H = A * (ctgα + ctgβ) / 2;

• M + H = D * (ctgα + ctgβ) / 2.

3. Kudzera kutalika ndi opendekera ngodya therebetween. Mwachitsanzo, D1 ndi D2 - opendekera wa trapezium ya; α, β - ngodya pakati pawo:

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

4. Mu malo ndi kutalika: M = R / N.