Kodi kupeza kutalika trapezoid chiyani?

Mu miyoyo yathu nthawi ifenso timalimbana ndi ntchito Masamu kuchita, monga kumanga. Pakati akalumikidzidwa ambiri zojambula, pali oimba ng'oma pamodzi. Ndi kuonetsetsa kuti ntchito yayenda bwino ndi wokongola, muyenera mawerengedwe yake molondola mbali pa chithunzi choterocho.

ndi chimene Mwalawafungulo? Izi quadrilateral otukukira kunja omwe ali ndi awiri mbali yomweyi, amatchedwa m'munsi mwa trapezoid ndi. Koma pali zinthu ziwiri zimene kulumikiza mfundo zimenezi. Iwo amatchedwa lateral. Imodzi mwa nkhani zokhudza chithunzi ichi, iyo ili: "Kodi kupeza kutalika trapezoid ndi" Monga ayenera kulabadira kutalika - mbali kumene kumatsimikizira mtunda kuchokera m'munsi wina ndi mzake. Pali njira zingapo kudziwa mtunda imeneyi, malinga zosintha kudziwika.

1. Mumadziwika zedi a zapansi zonse, b kutanthauza iwo ndi K, komanso dera trapezoid ndi. Kugwiritsa ntchito mfundo za amadziwika kuti mupeze kutalika kwa trapezoid, mu nkhani iyi mosavuta. Monga anatsimikiza Masamu a, m'dera trapezoid kuchita masamu kuti tinachita Uwerenge theka la m'munsi ndi kutalika. Kuyambira chilinganizo ichi mosavuta amapeza phindu ankafuna. Kuti tichite zimenezi, gawani m'dera kuchuluka theka la malo. Dongosolo amaonekera izi:

S = ((b + k) / 2) * H, apa H = S / ((b + k) / 2) = 2 * S / (b + k)

2. Mumadziwika kutalika midline, ife amatanthauza anthu d, ndi lalikulu. Kwa amene simukudziwa, mzere pakati ndi mtunda pakati pa midpoints a m'mbali. Kodi kupeza kutalika kwa trapezoid mu nkhani iyi? Malinga trapezoid katundu, mzere pakati limafanana ndi kuchuluka theka la zapansi, i.e. D = (b + k) / 2. Ife amachita chilinganizo lalikulu. Kuchotsa kuchuluka theka la m'munsi pa mtengo wa mzere pakati timapeza zotsatirazi:

S = D * H

Monga Tingaone chilinganizo kupeza mosavuta kwambiri anadziŵa msinkhu. Nagawira m'dera pa midline wa kufunika, tidzapeza kuchuluka osadziwika. Tilembere chilinganizo izi:

H = S / D

3. Mumadziwika kutalika kwa mbali imodzi (b) ndi mbali unali pakati pa mbali ndi m'munsi waukulu. Yankho la funso mmene kupeza kutalika trapezoid ndi, ndi nkhaniyi. Taganizirani trapezoid ABCD, kumene AB ndi CD ndi mbali lateral, mmene AB = b. M'munsi yaikulu ndi AD. Mbali anapanga ndi AB ndi AD ndiwo amaimira α. Mfundo B sanatchule kutalika H pa AD m'munsi. Tsopano tiyeni tione chifukwa makona ABF, lomwe ndi anayi. Mbali AB ndi hypotenuse, ndi BF-mwendo. Kuyambira katundu makona bwino chiŵerengero mtengo cathetus ndi hypotenuse limafanana ndi mtengo wa sine a mbali ya cathetus zosiyana (BF). Choncho, pamwamba, ndi kudziwa kutalika kwa trapezoid ndi kuchulukitsa phindu la mbali zina ndi sine wa α njingayo. Dongosolo ndi uyu motere:

H = b machimo (α)

4. Mofananamo, ngati ndi odziwika kukula kwa mbali ndi mbali amaimira β, unali pakati pa mbali ndi ang'onoang'ono m'munsi. Pothetsa ngati vuto, mbali pakati pa mbali ya kutalika kudziwika ndi umachitika 90 ° - β. Kuchokera katundu wa Triangles - chiŵerengero kutalika cathetus ndi hypotenuse limafanana ndi cosine ya njingayo unali pakati pa iwo. Kuyambira chilinganizo izi n'zosavuta tikuona kufunika kutalika:

H = b * Ko (β-90 °)

5. Kodi kupeza kutalika trapezoid, ngati zodziwika kokha kwa utali wozungulira bwalo alembedwa? Kuchokera tanthauzo la bwalo, izo nkhawa ina iliyonse m'munsi. Komanso, mfundo izi limagwirizana ndi malo a bwalo. Kuchokera pamenepa, ndizoonekeratu kuti mtunda pakati pawo ndi awiri, ndipo pa nthawi yomweyo, kutalika trapezoid ndi. Izo zikuwoneka ngati izi:

H r Mukhoza = 2 *

6. Nthawi zambiri pali ntchito zimene muyenera kupeza kutalika ndi trapezoid isosceles. Kumbukirani kuti trapezoid ndi mbali ofanana akutchedwa isosceles. Kodi kupeza kutalika kwa isosceles trapezoid? Ngati diagonals ndi perpendicular kutalika ndi wofanana ndi ndalama theka la zapansi lapansi.

Koma zoyenera kuchita ngati diagonals si perpendicular? Taganizirani isosceles trapezoid ABCD. Malinga ndi katundu, zapansi ndi kufanana. Kuchokera pamenepa, ndizoonekeratu kuti onse kumathandiza kupeza ngodya zabwino pa m'munsi adzakhala ofanana. Jambulani pamwamba awiri BF ndi cm. Potengera zimene takambiranazi, akhoza amanena kuti Triangles ABF ndi DCM ngofanana, kuti ali, AF = DM = (AD - BC) / 2 = (bk) / 2. Tsopano, zochokera zikhalidwe za vuto umakhala zedi ndi odziwika, kenako kupeza okwera, kutenga nkhani ya katundu onse a trapezoid isosceles.