Ovundlile trapezoid equilateral. Uyini umugqa phakathi trapezoid. Izinhlobo trapezoids. Esishwibweni - ke ..

Esishwibweni - icala olukhethekile quadrangle, lapho omunye pair of izinhlangothi kuhambisana. Igama elithi "trapezoid" lisuselwe kwelesiLatini elithi igama lesiGreki elithi τράπεζα, okusho "etafuleni", "etafuleni". Kulesi sihloko sizohlola izinhlobo esishwibweni and izakhiwo zalo. Futhi, sibheka indlela ukubala izakhi ngazinye sibalo Jomethri. Ngokwesibonelo, diagonal i trapezium equilateral, phakathi umugqa, endaweni nabanye. Indaba eziqukethwe aphansi geometry isitayela ethandwa, t. E. Ngendlela kalula.

Uhlolojikelele

Okokuqala, ake uqonde ukuthi quadrangle. Lesi sibalo icala olukhethekile ipholigoni kokuba izinhlangothi ezine kanye vertices ezine. Amabili vertices we quadrilateral, engewona nokho eduze, ngokuthi okuphambene. I Kungashiwo okufanayo amabili ezinhlangothini ze-non-eduze. Izinhlobo ezinkulu quadrangles - a parallelogram, isikwele, rhombus, sikwele, trapezoid futhi deltoid.

Ngakho emuva esishwibweni. Njengoba sishilo, lesi sibalo izinhlangothi ezimbili kukhona ngokulinganisa. Ziyakwazi ezibizwa ngokuthi yizisekelo. Lezi ezinye ezimbili (non-parallel) - ezinhlangothini. Mathiriyeli ukuhlolwa ahlukahlukene neluhlolo ngokuvamile kakhulu ungakwazi ukuhlangabezana nezinselele ezihlobene trapezoids kabani isixazululo ngokuvamile kudinga ulwazi yomfundi engamboziwe uhlelo. School Course geometry yethula abafundi engeli izakhiwo kanye diagonals kanye umugqa imidiyeni i trapezoid isosceles. Kodwa ngaphandle ukuthi okukhulunywa kumumo weJiyomethri unezinye izici. Kodwa ngazo kamuva ...

izinhlobo esishwibweni

Kunezinhlobo eziningi lesi sibalo. Nokho, ngokuvamile kakhulu wesiko sicabangele ezimbili - isosceles futhi unxande.

1. trapezoid kukanxande - figure lapho omunye izinhlangothi perpendicular isizinda. Uneziqu engeli amabili zihlale elilingana degrees ayisishiyagalolunye.

2. isosceles trapezium - sibalo Jomethri kabani izinhlangothi bayalingana. Ngakho, kanye nama-engeli ngasesinqeni futhi bayalingana.

Izimiso eziyinhloko izindlela sokutadisha izakhiwo trapezoid

Izimiso eziyisisekelo zihlanganisa ukusetshenziswa okuthiwa umsebenzi indlela. Eqinisweni, asikho isidingo ukungena theory Yiqiniso Jiyomethri izakhiwo entsha yalesi sibalo. Zingaba evulekile noma inqubo yokwenza imisebenzi ehlukahlukene (uhlelo kangcono). Kubalulekile kakhulu ukuthi uthisha wazi ukuthi imisebenzi udinga ukubeka phambi abafundi nganoma isiphi isikhathi yenqubo yokufunda. Ngaphezu kwalokho, impahla ngayinye trapezoid kungenziwa imelelwa umsebenzi ukhiye ohlelweni msebenzi.

Isimiso sesibili iyona okuthiwa inhlangano Kuvunguza cwaningo "emangalisayo" esishwibweni izakhiwo. Lokhu kusho ukubuyela inqubo yokufunda izici ngamunye sibalo Jomethri. Ngakho, abafundi kulula ukuthi uwakhumbule. Ngokwesibonelo, impahla amaphuzu amane. Kungaba luhlolwe njengoba ekuhloleni ukufana futhi kamuva usebenzisa zithwala. A onxantathu Equal eseduze izinhlangothi sibalo, kungenzeka ukufakazela ngokusebenzisa hhayi kuphela izindawo onxantathu kanye eziphakeme alinganayo olwenziwa ezinhlangothini zazo amanga emgceni locondzile, kodwa futhi ngokusebenzisa S ifomula = 1/2 (ab * sinα). Ngaphezu kwalokho, kungenzeka ukuba kuvelwe umthetho Sines kuya trapezium olotshiwe noma unxantathu wesokudla-angled futhi trapezoid ezichazwe t. D.

Ukusetshenziswa "yangemva" sibonisa sibalo Jomethri okuqukethwe Yiqiniso esikoleni - a tasking ngemfundiso yabo ubuchwepheshe. inkomba njalo ukufunda property ukudlula ezinye kuvumela abafundi ukuba bafunde esishwibweni ezijulile futhi kuqinisekisa ekuphumeleleni kwalo msebenzi. Ngakho, thina uqhubekele ezifundwa sibalo emangalisayo.

Elements nezakhiwo i trapezoid isosceles

Njengoba sesiphawulile, kule sibalo Jomethri izinhlangothi bayalingana. Nokho it is njengoba trapezoid kwesokudla ezaziwayo. Futhi kuyini na kuphawuleka kakhulu futhi kungani lethiwa? Izici ezikhethekile kwalesi sibalo uyalandisa ukuthi unakho amacala alingane hhayi kuphela futhi angles ngasesinqeni, kodwa futhi ngokuphambeneyo. Ngaphezu kwalokho, isamba engeli ye-trapezoid isosceles ilingana 360. Kodwa lokho akuyona yonke! Kuphela emhlabeni isosceles lingachazwa ngumuntu umbuthano wabo bonke trapezoids ezaziwayo. Lokhu kungenxa yokuthi isamba engeli okuphambene kule sibalo 180 degrees, futhi kuphela ngaphansi kwalesi simo lingachazwa ngokuthi indulungu quadrangle. I Izakhiwo ezilandelayo sibalo Jomethri wukuthi ibanga kusuka phezulu kumila kuya Iwumbono iziqongo aphikisanayo emgqeni equkethe lokhu base kuyoba ulingana umugca losemkhatsini esifubeni.

Manje ake sibheke indlela ukuthola amakhona i trapezoid isosceles. Cabanga ikhambi lale nkinga, uma nje ubukhulu amaqembu sibalo ezaziwayo.

isinqumo

Kuyisiko ukupha abashadayo isho izincwadi quadrangle A, B, C, D, lapho BS futhi BP - isisekelo. Esimeni trapezoid isosceles izinhlangothi bayalingana. Sicabanga ukuthi ubungako bawo kulingana X Y Ubukhulu kukhona elisekela futhi Z (lokuncane okukhulu, ngokulandelana). Sokubalwa engela isidingo ukuchitha ekuphakameni H. Umphumela uba unxantathu wesokudla-angled ABN lapho AB - the hypotenuse, futhi BN futhi AN - imilenze. Bala usayizi umlenze AN: ukhupha kusukela base emikhulu incane khona, futhi umphumela lihlukaniswe by 2. bhala ifomula: (ZY) / 2 = F. Manje, ukubala engela okukhulu unxantathu ukusetshenziswa umsebenzi cos. Thina ukuthola ukungena okulandelayo: cos (β) = X / F. Manje kubalwe i-engeli: β = Arcos (X / F). Ngaphezu kwalokho, ukwazi eyodwa ekhoneni, singakwazi ukuthola nelesibili, ukwenza lo msebenzi aphansi izibalo: 180 - β. Zonke engeli kuchazwa.

Kukhona isixazululo yesibili yale nkinga. Ekuqaleni sokususwa kusuka ekhoneni ekuphakameni umlenze N. sinquma ukubaluleka kwengosi kuba BN. Siyazi ukuthi esigcawini hypotenuse unxantathu kwesokudla ilingana isamba sezikwele ezinye izinhlangothi ezimbili. Sithola: BN = √ (X2 F2). Ngokulandelayo, sisebenzisa Trigonometric umsebenzi TG. Umphumela: β = arctg (BN / F). I-engeli acute kutholakala. Okulandelayo, sichaza engela obtuse njengasezulwini indlela yokuqala.

Impahla diagonals i trapezoid isosceles

Okokuqala, sibhala imithetho emine. Uma idayagonali zibe trapezoid isosceles kukhona perpendicular ke:

- ukuphakama sibalo ilingana nenani lezinombolo elisekela, zihlukaniswe amabili;

- ukuphakama kwalo kanye umugqa phakathi bayalingana;

- indawo trapezoid uyalingana skwele ukuphakama (isikhungo umugqa elisekela isigamu);

- esigcawini idayagonali kwesikwele ilingana isigamu isamba kabili lezisekelo isikwele noma umugcamkhatsi (ukuphakama).

Manje sibheke ifomula belinganisa idayagonali i trapezoid equilateral. Le piece of ulwazi kungenziwa ihlukaniswe yaba izingxenye ezine:

1. Umthetho ofingqiwe obuphelele idayagonali ngokusebenzisa uhlangothi lwalo.

Sicabanga ukuthi A - isisekelo ephansi, B - Top, C - amacala alingane, D - idayagonali. Kulokhu, ubude kungaba azimisele ngendlela elandelayo:

D = √ (C 2 + A * B).

2. Umthetho ofingqiwe ngobude diagonal cosine.

Sicabanga ukuthi A - isisekelo ephansi, B - Top, C - amacala alingane, D - idayagonali, α (ngasesinqeni engezansi) kanye β (base engenhla) - emakhoneni trapezoid. We ukuthola le ndlela elandelayo, ngawo umuntfu angakhona kubala ubude idayagonali:

- 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. Umthetho ofingqiwe obuphelele idayagonali i trapezoid isosceles.

Sicabanga ukuthi A - isisekelo ephansi, B - engenhla, D - idayagonali, M - umugqa phakathi H - ukuphakama, P - indawo trapezoid, α futhi β - igebe eliphakathi diagonals. Nquma ubude amafomula ezilandelayo:

- D = √ (M2 + N2);

- D = √ (H 2 + (A + B) 2/4);

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

Ngenxa yalesi simo, ukulingana: sinα = sinβ.

4. Formula obuphelele idayagonali emaceleni futhi ukuphakama.

Sicabanga ukuthi A - isisekelo ephansi, B - Top, C - izinhlangothi, D - idayagonali, H - ukuphakama, α - engela sizindza aphansi.

Nquma ubude amafomula ezilandelayo:

- D = √ (H 2 + (A-P * ctgα) 2);

- D = √ (H 2 + (B + F * ctgα) 2);

- D = √ (A2 + S2-2A * √ (C2-H2)).

Elements nezakhiwo a trapezium unxande

Ake sibheke ukuthi abanesithakazelo kule sibalo Jomethri. Njengoba sishilo, siba trapezoid unxande engeli amabili kwesokudla.

Ngaphandle kwencazelo classical, kukhona abanye. Ngokwesibonelo, trapezoid elingunxande - a trapezoid lapho uhlangothi kuba perpendicular isizinda. Noma balolonge kokuba eceleni engele. Kulesi hlobo trapezoids height olungaphezu perpendicular elisekela. Umugqa maphakathi - ingxenye lebhokisi kwe-Midpoints izinhlangothi ezimbili. Impahla isici kusho ukuthi kuyinto parallel lezisekelo futhi ilingana kwesigamu sum yabo.

Manje ake sicabangele amafomula eziyisisekelo ezichaza ngamajamo weJiyomethri. Ukuze wenze lokhu, sicabanga ukuthi A no B - isizinda; C (perpendicular isizinda) kanye D - izinhlangothi trapezium elingunxande, M - umugqa phakathi, α - engela oyingozi, P - ndawo.

1. uhlangothi perpendicular lezisekelo, sibalo ilingana ukuphakama (C = N), futhi silingana nobude wesibili ohlangothini A no-sine ye-α engela ngesikhathi base enkulu (C = A * sinα). Ngaphezu kwalokho, kuyinto ilingane umkhiqizo tangent ye-acute engela α futhi umehluko elisekela: C = (A-B) * tgα.

2. D ohlangothini (hhayi perpendicular isizinda) ilingane quotient umehluko of A no B kanye cosine (α) noma engela abukhali ukuphakama yangasese izibalo H futhi sine engela oyingozi: A = (A-B) / cos α = C / sinα.

3. olungaphezu perpendicular lezisekelo, ilingana impande skwele esigcawini umehluko D - ehlangothini lwesibili - futhi isikwele base umehluko:

C = √ (Q2 (A-B) 2).

4. Side A trapezoid unxande ilingana impande skwele isamba skwele uhlangothi isikwele C elisekela weJiyomethri ukuma umehluko: D = √ (C 2 + (A-B) 2).

5. Uhlangothi C uyalingana quotient kwesikwele double isamba Izisekelo zawo: C = P / M = 2P / (A + B).

6. Le ndawo ebizwa ngokuthi M umkhiqizo (emgqeni maphakathi trapezoid unxande) ukuphakama noma isiqondiso lateral perpendicular elisekela: P = M * N = M * C

7. Isikhundla C quotient kabili ukuma square umkhiqizo engela sine oyingozi futhi isamba Izisekelo zawo: C = P / M * sinα = 2P / ((A + B) * sinα).

8. Umthetho ofingqiwe uhlangothi trapezium unxande ngokusebenzisa idayagonali yayo, futhi igebe eliphakathi kwabo:

- sinα = sinβ;

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

lapho D1 futhi D2 - diagonal we trapezoid; α futhi β - igebe eliphakathi kwabo.

9. Formula ohlangothini ngokusebenzisa engela ngasesinqeni aphansi nabanye: A = (A-B) / cosα = C / sinα = H / sinα.

Kusukela trapezoid nge engele kwesokudla icala ethile trapezoid, omunye amafomula ukuthi ukucacisa lezi zibalo, uzohlangana ne unxande.

Izakhiwo incircle

Uma isimo Kuthiwa ngendlela unxande trapezoid elalibhalwe umbuthano ke ungasebenzisa Izakhiwo ezilandelayo:

- inani base yinani emaceleni;

- ibanga kusuka phezulu ukuma unxande amaphuzu tangency kwendilinga elalibhalwe uhlale alinganayo;

- ukuphakama trapezoid ilingana ohlangothini, perpendicular lezisekelo, ilingana kuya ububanzi we umbuthano ;

- isikhungo Umbuthano iphuzu lapho aphambana bisectors ka-engeli ;

- uma ohlangothini lateral we iphuzu contact sehlukaniswe ubude N-M, ke engaba umbuthano ilingana impande skwele umkhiqizo yalezi izingxenye;

- quadrangle ezakhiwe amaphuzu contact, phezulu trapezoid kanye maphakathi umbuthano elalibhalwe - it is a sikwele, kabani lobani ilingane engaba;

- indawo bangamaphesenti umkhiqizo isizathu futhi umkhiqizo nenxenye isamba elisekela ibambene phezulu.

esishwibweni Okufanayo

Lesi sihloko iyasiza ukutadisha izakhiwo izibalo weJiyomethri. Ngokwesibonelo, ukuhlukaniswa idayagonali ku onxantathu ezine trapezoid, futhi eduze kumila okunjalo, futhi izinhlangothi - of alinganayo. Lesi sitatimende kungenziwa ngokuthi isakhiwo onxantathu, okuyinto esishwibweni eziphukile diagonals yayo. Ingxenye yokuqala yalesi sitatimende kubonakaliswa ngokusebenzisa uphawu ukufana kwamazwi emakhoneni ezimbili. Ukuze afakazele ingxenye yesibili kungcono ukusebenzisa indlela echazwe ngezansi.

ubufakazi

Yamukela ukuthi ABSD sibalo (AD futhi BC - ngesisekelo trapezoid) kuyinto diagonals eziphukile HP futhi AC. Iphuzu empambana - O. Sithola onxantathu ezine: AOC - ngasesinqeni ephansi, BOS - base engenhla, ABO futhi wapheka emaceleni. Triangles wapheka futhi biofeedback abe ukuphakama ezivamile kulelo cala, uma izingxenye BO futhi OD kukhona lezisekelo zawo. Sithola ukuthi umehluko ezindaweni zabo (P) elilingana umehluko kulezi izingxenye: PBOS / PSOD = BO / ML = K. Ngenxa yalokho, PSOD = PBOS / K. Ngokufanayo, aboncantathu AOB futhi biofeedback abe ukuphakama ezivamile. Wamukele i-base yabo izingxenye SB futhi OA. We ukuthola PBOS / PAOB = CO / OA = K futhi PAOB = PBOS / K. Kule kusobala ukuthi PSOD = PAOB.

Ukuhlanganisa abafundi impahla bayakhuthazwa ukuthola ukuxhumana phakathi izindawo onxantathu etholwe, okuyinto esishwibweni eziphukile diagonals yayo, kokunquma umsebenzi olandelayo. Kuyaziwa ukuthi onxantathu BOS futhi Adp izindawo bayalingana, kubalulekile ukuthola kwendawo trapezoid. Njengoba PSOD = PAOB ke PABSD PBOS + = PAOD + 2 * PSOD. Kusukela ukufana onxantathu BOS futhi ANM kulandela ukuthi BO / OD = √ (PBOS / PAOD). Ngenxa yalokho, PBOS / PSOD = BO / OD = √ (PBOS / PAOD). Thola PSOD = √ (* PBOS PAOD). Khona-ke PABSD PBOS + = PAOD + 2 * √ (PAOD PBOS *) = (+ √PBOS √PAOD) 2.

izakhiwo ukufana

Ukuqhubeka ukuthuthukisa le timu, kungenzeka ukufakazela, kanye nezinye izici ezithakazelisayo trapezoids. Ngakho, ngosizo ukufana ingaqinisa ingxenye impahla, okuyinto sidlula iphuzu ezakhiwe empambana we diagonals sibalo Jomethri, zifana kuya phansi. Ngokuba lokho sikusho ukuxazulula inkinga elandelayo: kubalulekile ukuthola obuphelele RK ingxenye okudlula iphuzu O. Kusukela ukufana onxantathu Adp futhi SPU kulandela ukuthi AO / OS = AD / BS. Kusukela ukufana onxantathu Adp futhi ASB kulandela ukuthi AB / AC = PO / AD = BS / (BP + BS). Lokhu kusho ukuthi BS * PO = AD / (AD + BC). Ngokufanayo, kusukela ukufana onxantathu MLC futhi Abr kulandela ukuthi Kulungile * BP = BS / (BP + BS). Lokhu kusho ukuthi OC futhi RC = RC = 2 * BS * AD / (AD + BC). Ingxenye edabula iphuzu empambana we diagonals parallel base nokuxhuma izinhlangothi ezimbili, iphuzu kuhlangana uhlukanise ngesigamu. ubude bayo - iyona kusho harmonic okucabanga izibalo.

Cabangela izici ezilandelayo we trapezoid, okuthiwa impahla amaphuzu amane. iphuzu empambana we diagonals (D), empambana ukuqhubeka izinhlangothi (E) kanye maphakathi no-elisekela (T ne-G) njalo amanga emgqeni efanayo. Kulula ukufakazela indlela ukufana. I onxantathu eziba umphumela kuyizipho Bes ezifanayo futhi AED, futhi ngamunye uqukethe okuthile okungase lesemkhatsini ET futhi DLY ukwehlukana engela isihloko E ezingxenyeni alinganayo. Ngakho, iphuzu E, T F kukhona collinear. Ngokufanayo, emgqeni efanayo ahlelwe ngokuya T, Jehova, G. Lokhu kulandela kusukela ukufana onxantathu BOS futhi ANM. Ngakho sicina ngokuthi wonke amagama amane - E, T, O futhi F - Bazolala emgceni locondzile.

Ukusebenzisa trapezoids efanayo, tingafundziswa ukuze abafundi ukuthola ubude ingxenye (LF), okuyinto uhlukanisa sibalo ku ezimbili ezinjengezewundlu. Lokhu Imi kumele kube parallel izisekelo. Kusukela wathola trapezoid ALFD LBSF futhi efanayo, BS / LF = LF / AD. Lokhu kusho ukuthi LF = √ (BS * BP). Siphetha ngokuthi ingxenye ukuthi ihlukane trapezium ezimbili njengewundlu, has a ubude ilingana kusho Jomethri ye ubude elisekela ukuthola.

Cabanga impahla elandelayo ukufana. Kusekelwe ingxenye ukuthi uhlukanisa trapezoid ku alinganayo usayizi izingcezu ezimbili. Yamukela ukuthi ingxenye esishwibweni ABSD ihlukaniswe ezimbili EH efanayo. Kusukela phezulu B ehlisela ukuphakama ukuthi ingxenye ihlukaniswe yaba izingxenye ezimbili EN - B1 kanye B2. Thola PABSD / 2 = (BS + EH) * V1 / 2 = (AP + EH) * B2 / 2 = PABSD (BP + BS) * (B1 + B2) / 2. Ngaphezu kwalokho ukuqamba uhlelo, lapho ezothando lokuqala (BS + EH) * B1 = (BP + EH) * B2 futhi yesibili (BS + EH) * B1 = (BP + BS) * (B1 + B2) / 2. Lokho kusho ukuthi B2 / B1 = (BS + EH) / (BP + EH) kanye BS + EH = ((BS + BP) / 2) * (1 + B2 / B1). Sithola ukuthi ubude sokuhlukanisa trapezoid ku amabili alinganayo, ilingana ubude isilinganiso lezisekelo quadratic: √ ((CN2 + aq2) / 2).

ukufana iziphetho

Ngakho, siye wafakazela ukuthi:

1. ingxenye yokuxhuma phakathi trapezoid emaceleni lateral, zifana kuya BP kanye BS futhi BS yiyona izibalo Kusho futhi BP (base ubude trapezoid).

2. Ibha edabula iphuzu O ka empambana we diagonals AD kuqondane and BC kuyoba ilingane harmonic izinombolo kusho BP kanye BS (2 * BS * AD / (AD + BC)).

3. ingxenye agqekeze trapezoid efanayo has a obuphelele weJiyomethri kusho elisekela BS futhi BP.

4. I element ehlukanisa komumo usayizi amabili alinganayo, ubude kusho izinombolo square BP kanye BS.

Ukuhlanganisa impahla nokuqaphela Ukuxhumana phakathi izingxenye umfundi kuyadingeka ukwakha kubo trapezoid ethize. Yena kalula sibonise line isilinganiso kanye ingxenye okudlula iphuzu - empambana we diagonals izibalo - parallel phansi. Kodwa lapho kuyoba wesithathu nowesine? Le mpendulo kuzoholela umfundi ukuba kokutholakala ubuhlobo ongaziwa phakathi kumanani esilinganiso.

Ingxenye kokujoyina kwe-Midpoints we diagonals we trapezoid

Cabanga impahla ezilandelayo sibalo. Samukela ukuthi MN ingxenye parallel lezisekelo bahlukanise ngesigamu ngokuphambeneyo. iphuzu kuhlangana ngokuthi W futhi S. Lokhu ingxenye kuyoba ulingana isigamu isizathu umehluko. Ake sihlole ngokuningiliziwe ngalokhu. Msh - emgqeni isilinganiso ABS unxantathu, kuba ilingane BS / 2. Minigap - umugqa phakathi DBA unxantathu, kuba elilingana AD / 2. Khona-ke sithola ukuthi SHSCH = minigap-msh ke SHSCH = AD / 2-BS / 2 = (AD + BC) / 2.

maphakathi gravity

Ake sibheke ukuthi uwuchaza kanjani isici esithile esinikeziwe sibalo Jomethri. Ukuze wenze lokhu, kumele ukunweba ayehlala kuwo lapho ekuleso oluyi. Kusho ukuthini? Kuyadingeka ukwengeza isizinda kuya phansi engenhla - kunoma yiziphi izinhlangano, isibonelo, ilungelo. A aphansi isikhathi ubude phezulu kwesokunxele. Okulandelayo, xhuma idayagonali yabo. Iphuzu empambana kulesi sigaba ngolayini maphakathi sibalo maphakathi yesisindo trapezium.

Masingasuki futhi kuchazwe esishwibweni

Ake uhlu izici ezifana izibalo:

1. Line kungenziwa alotshiwe umbuthano kuphela uma kuba isosceles.

2. Emhlabeni umbuthano lingachazwa ngokuthi i-trapezoid, inqobo nje uma isamba ubude lezisekelo zawo yinani lika ubude izinhlangothi.

Imiphumela emjikelezweni olotshiwe:

1. ukuphakama trapezoid echazwe njalo ulingana kabili engaba.

2. Uhlangothi trapezoid echazwe ibhekwa kusukela maphakathi mbuthano ngo-engeli kwesokudla.

Umphumela wokuqala isobala, futhi ibonise yesibili liyadingeka ukusungula ukuthi engela wapheka sishiwo ngokuqondile, okungukuthi, eqinisweni, nakho kungase kungabi lula. Kodwa ngokwazi impahla ikuvumela ukuba usebenzise unxantathu kwesokudla ukuze uxazulule izinkinga.

Manje thina ucacise phetho trapezoid isosceles, eqoshwe kumbuthano. We ukuthola ukuthi height weJiyomethri kusho sibalo elisekela: H = 2R = √ (BS * BP). Ukufeza indlela eyisisekelo zokuxazulula izinkinga ngoba trapezoids (isimiso ezimbili eziphakeme), umfundi kufanele ukuxazulula umsebenzi elandelayo. Yamukela ukuthi BT - ukuphakama isosceles izibalo ABSD. Udinga ukuthola elula of IAT AP. Ukusebenzisa ifomula ezichazwe ngenhla, oyokwenza akunzima.

Manje ake sichaze nendlela yokuzigwema ukuze sithole engaba umbuthano kwendawo echazwe trapezoid. Ivinjelwe kusuka phezulu B ukuphakama phezu isizinda BP. Kusukela umbuthano alotshiwe trapezoid, le BS + 2AB = BP noma AB = (BS + BP) / 2. Kusukela unxantathu ABN yokuthola sinα = BN / 2 * AB = BN / (AD + BC). PABSD = (BS + BP) BN * / 2, BN = 2R. Thola PABSD = (BP + BS) * R, kusobala ukuthi R = PABSD / (AD + BC).

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Wonke amafomula umugcamkhatsi esishwibweni

Manje sekuyisikhathi ukuya into yokugcina yalesi sibalo Jomethri. Sizokwenza ukuqonda, uyini umugqa phakathi trapezoid (M):

1. Ngokusebenzisa lezisekelo: M = (A + B) / 2.

2. Ngemva ukuphakama, base namakhona:

• M-H = A * (ctgα + ctgβ) / 2;

• M + H = D * (ctgα + ctgβ) / 2.

3. Ngokusebenzisa ukuphakama idayagonali engela therebetween. Ngokwesibonelo, D1 futhi D2 - diagonal we trapezium; α, β - igebe eliphakathi kwabo:

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

4. Ngaphakathi kwendawo futhi ukuphakama: M = R / N.