He aha ka trapezoid: wehewehe, ʻano, waiwai

Ma kēia hoʻolaha, e noʻonoʻo mākou i ka wehewehe ʻana, nā ʻano a me nā waiwai (e pili ana i nā diagonal, nā kihi, ka waena waena, kahi intersection o nā ʻaoʻao, etc.) o kekahi o nā ʻano geometric nui - he trapezoid.

Ka wehewehe ʻana o kahi trapezoid

Trapezium He ʻaoʻao ʻehā, ʻelua mau ʻaoʻao i kūlike a ʻo nā ʻaoʻao ʻelua ʻaʻole.

Ua kapaia na aoao like nā kumu o kahi trapezoid (AD и BC), na aoao elua aoao (AB a me CD).

Angle ma ke kumu o ka trapezoid - ka huina kūloko o kahi trapezoid i hana ʻia e kona kumu a me kona ʻaoʻao, no ka laʻana, α и β.

Ua kākau ʻia kahi trapezoid ma ka helu ʻana i kona mau vertices, ʻo ka pinepine kēia ABCD. A ua hōʻike ʻia nā kumu e nā leka Latin liʻiliʻi, no ka laʻana, a и b.

laina waena o ka trapezoid (MN) – he mahele e hookui ana i na kiko waena o kona mau aoao aoao.

Kiʻekiʻe Trapeze (h or BK) he kiko pololei i kaha ʻia mai kekahi kumu a i kekahi kumu.

Nā ʻano trapezium

Isosceles trapezoid

ʻO kahi trapezoid nona nā ʻaoʻao like i kapa ʻia ʻo isosceles (a i ʻole isosceles).

AB = CD

Trapezium huinahāhā

ʻO kahi trapezoid, kahi i pololei nā kihi ʻelua ma kekahi o kona ʻaoʻao ʻaoʻao, ua kapa ʻia ʻo ia he ʻaoʻao.

∠BAD = ∠ABC = 90°

Trapezoid nui

He scalene ka trapezoid inā ʻaʻole like kona mau ʻaoʻao a ʻaʻole pololei kekahi o nā kihi kumu.

Na waiwai trapezoidal

ʻO nā waiwai i helu ʻia ma lalo nei e pili ana i kēlā me kēia ʻano trapezoid. Hōʻike ʻia nā waiwai a me nā trapezoid ma kā mākou pūnaewele i nā puke ʻokoʻa.

Waiwai 1

He 180° ka huina o na kihi o ka trapezoid e pili ana i ka aoao hookahi.

α + β = 180°

Waiwai 2

Ua like ka laina waena o ka trapezoid me kona mau kumu a ua like ia me ka hapalua o ko lakou huina.

Waiwai 3

Aia ka māhele e hoʻopili ai i nā kiko waena o nā diagonal o kahi trapezoid ma kona laina waena a ua like ia me ka hapalua o ka ʻokoʻa o nā kumu.

• KL he māhele laina e hui ana i nā kiko waena o nā diagonal AC и BD
• KL aia ma ka laina waena o ka trapezium MN

Waiwai 4

ʻO nā kiko o ka hui ʻana o nā diagonal o ka trapezoid, nā hoʻonui o kona mau ʻaoʻao a me nā kiko waena o nā kumu e moe ana ma ka laina pololei like.

• DK - hoʻomau o ka ʻaoʻao CD
• AK - hoʻomau o ka ʻaoʻao AB
• E – waena o ke kumu BCIe BE = EC
• F – waena o ke kumu ADIe AF = FD

Ina he 90° ka huina o na huina ma kekahi kumu (oia ∠DAB + ∠ADC u90d XNUMX °), ʻo ia hoʻi ka hoʻonui ʻana o nā ʻaoʻao o ka trapezoid i ke kihi ʻākau, a me ka ʻāpana e hoʻopili ai i nā kikowaena waena o nā kumu (ML) ua like ia me ka hapalua o ko lakou okoa.

Waiwai 5

Na na diagonal o ka trapezoid e puunaue ia ia i 4 huinakolu, elua o ia mau huinakolu (ma na kumu), a o na mea elua (ma na aoao) ua like ma .

• ΔAED ~ ΔBEC
• S_ΔABE =S_ΔCED

Waiwai 6

Hiki ke hōʻike ʻia kahi ʻāpana e hele ana ma ka huina o nā diagonal o kahi trapezoid e like me kona mau kumu ma ke ʻano o ka lōʻihi o nā kumu:

Waiwai 7

ʻO nā ʻāpana ʻāpana o nā ʻaoʻao o kahi trapezoid me ka ʻaoʻao ʻaoʻao hoʻokahi, ua kū like ʻia.

• AP – ʻāpana ʻāpana ∠ INO
• BR – ʻāpana ʻāpana ∠ABC
• AP pihi BR

Waiwai 8

Hiki ke kahakaha ʻia ka pōʻai i loko o ka trapezoid inā like ka huina o nā lōʻihi o kona mau kumu me ka huina o nā lōʻihi o kona mau ʻaoʻao.

ʻO kēlā mau mea. AD + BC = AB + CD

ʻO ka radius o ka pōʻai i kākau ʻia i loko o kahi trapezoid ua like ia me ka hapalua o kona kiʻekiʻe: R = h/2.