Indlela yokuthola ukuphakama trapezoid?

Ezimpilweni zethu ngokuvamile kakhulu esinakho ukubhekana ukusetshenziswa geometry practice, ezifana ukwakhiwa. Phakathi bobunjwa ezivamile weJiyomethri, kukhona esishwibweni. Futhi ukuqinisekisa ukuthi lo msebenzi waba yimpumelelo futhi enhle, udinga ukubala efanele futhi olunembile izici okwesikhathi onethonya.

Uyini Keystone? Lokhu quadrilateral ayizindunduma elinendawo pair of izinhlangothi okufanayo, ukubizwa ngokuthi kumila trapezoid. Kodwa kukhona nezinye izici ezimbili ukuxhuma zizathu. Zibizwa ngokuthi ama-lateral. Omunye ezithinta lesi sibalo, uthi: 'kanjani ukuthola ukuphakama trapezoid "Vele kudingeka ukuba banake ukuphakama - ingxenye ukuthi inquma ibanga kusuka base eyodwa kuya kwenye. Kunezindlela eziningana ukucacisa lokhu ibanga, kuye eziguquguqukayo ezaziwayo.

1. nenani Akwaziwa kokubili lezisekelo, b ubhekisele kuwo futhi k, kanye endaweni trapezoid. Ukusebenzisa amanani eyaziwa ukuthola ukuphakama trapezoid, kulesi simo kalula. Njengoba ubizwa kusukela geometry ezaziwayo, endaweni trapezoid ibalwa njengoba umkhiqizo isigamu isamba isizinda futhi ukuphakama. Kule ifomula kalula athola inani wayefisa. Ukuze wenze lokhu, uhlukanise indawo isigamu semali ngezizathu. Ngo ifomula zaziyoba ibukeke lokhu:

S = ((b + k) / 2) * h, lapha h = S / ((b + k) / 2) = 2 * S / (b + k)

2. obuphelele Akwaziwa of umugca losemkhatsini esifubeni, thina selisho d, futhi sikwele. Kulabo abazi, emgqeni phakathi ibanga phakathi kwe-Midpoints izinhlangothi. Indlela yokuthola ukuphakama trapezoid kuleli cala? Ngokusho impahla trapezoid, emgqeni phakathi oluhambisana isigamu semali elisekela, isb d = (b + k) / 2. Saphinde iphendukele ifomula sikwele. Njengoba ezothatha isikhundla isigamu inani base on ukubaluleka emgqeni phakathi, sithola lokhu okulandelayo:

S = d * h

Njengoba singabona kusukela ifomula etholwe ukuphakama esephetha kalula kakhulu. Kwehlukanisa endaweni ku umugca lohlukanisa emkhatsini yenani, siyothola ubuningi engaziwa. Sibhala le ifomula:

h = S / d

3. Ubude Akwaziwa kolunye uhlangothi (b) kanye engela obakhiwa hlangothi futhi base ngobukhulu. Impendulo yombuzo kanjani ukuthola ukuphakama trapezoid, futhi kulesi simo. Cabanga ABCD trapezoid, lapho AB futhi CD kukhona izinhlangothi lateral, lapho AB = b. Kumila ngobukhulu kuyinto AD. I-engeli ezakhiwe AB futhi AD luchazwa α. Kusukela endaweni B yeka h ukuphakama phezu isizinda AD. Manje cabanga unxantathu okuholela ABF, okuyinto elingunxande. Side AB iyona hypotenuse, futhi BF-umlenze. Kusukela impahla unxantathu wesokudla isilinganiso value cathetus kanye hypotenuse oluhambisana ukubaluleka sine ye-engela cathetus okuphambene (BF). Ngakho-ke, kokucabangela okushiwo ngenhla, ukubala ukuphakama trapezoid wande ukubaluleka isici esithile futhi sine ye-α-engeli. Ngo ifomula lokhu kanje:

h = b * isono (α)

4. Ngokufanayo, kunjalo uma usayizi eyaziwayo ecaleni kanye engela ezikhonjiswe β, obakhiwa hlangothi futhi base ezincane. Ekuxazululeni inkinga enjalo, i-engeli phakathi uhlangothi ukuphakama eyaziwa futhi ligcinwe 90 ° - β. Kusukela izakhiwo onxantathu - isilinganiso obuphelele cathetus kanye hypotenuse oluhambisana cosine ye-engeli kahle phakathi kwabo. Kule ifomula kulula baphethe ukuphakama Inani:

h = b * cos (β-90 °)

5. Indlela yokuthola ukuphakama trapezoid, uma aziwa yodwa kuze lo engaba umbuthano elalibhalwe? Kusukela kwencazelo mbuthano, kumayelana eyodwa iphuzu isizinda ngasinye. Ngaphezu kwalokho, la maphuzu ahambisana nendawo mbuthano. Kule kusobala ukuthi ibanga elibahlukanisile iyona ubukhulu, futhi ngesikhathi esifanayo, ukuphakama trapezoid. Kubonakala sengathi lokhu:

h = 2 * r

6. Ngokuvamile kukhona imisebenzi udinga ukuthola ukuphakama i trapezoid isosceles. Khumbula ukuthi trapezoid nge amacala alingane ibizwa ngokuthi i isosceles. Indlela yokuthola ukuphakama isosceles trapezoid? Uma diagonals kukhona ukuphakama perpendicular ilingana isigamu isamba elisekela.

Kodwa yini okufanele uyenze uma diagonals akuzona perpendicular? Cabanga ngalesi isosceles trapezoid ABCD. Ngokusho impahla yayo, lezisekelo kukhona ngokulinganisa. Kule kusobala ukuthi engele ngasesinqeni kuzolingana. Dweba ezimbili eziphakeme BF kanye CM. Ngokusekelwe osekushiwo, kungashiwo wagomela ukuthi onxantathu ABF futhi DCM bayalingana, okungukuthi, AF = DM = (AD - BC) / 2 = (bk) / 2. Manje, esekelwe nemibandela inkinga, ukuchaza izinto eziningi ezaziwa, bese uwuthole kokuwa, ikhumbula zonke izindawo i trapezoid isosceles.