Gịnị bụ trapezoid: nkọwa, ụdị, Njirimara

N'akwụkwọ a, anyị ga-atụle nkọwa, ụdị na ihe onwunwe (banyere diagonals, angles, midline, intersection point of the side, etc.) nke otu n'ime isi geometric shapes - trapezoid.

Nkọwa nke trapezoid

Ụdị trapezium bụ akụkụ anọ, akụkụ abụọ nke ha na-adakọ na nke ọzọ adịghị.

A na-akpọ akụkụ ndị yiri ya ntọala nke trapezoid (AD и BC), akụkụ abụọ nke ọzọ n'akụkụ (AB na CD).

Angle na ala nke trapezoid - akụkụ dị n'ime trapezoid kpụrụ site na isi ya na akụkụ ya, dịka ọmụmaatụ, α и β.

A na-ede trapezoid site n'ịdepụta vertices ya, ọtụtụ mgbe nke a bụ ABCD. A na-egosipụtakwa ntọala ndị ahụ site na obere mkpụrụedemede Latin, dịka ọmụmaatụ, a и b.

Ahịrị etiti nke trapezoid (MN) - akụkụ nke na-ejikọta etiti etiti nke akụkụ ya.

Trapeze Height (h or BK) bụ ihe kwụ ọtọ site n'otu ntọala gaa na nke ọzọ.

Ụdị trapezium

Ụdị trapezoid

A na-akpọ trapezoid nke akụkụ ya hà nhata bụ isosceles (ma ọ bụ isosceles).

AB = CD

Trapezium anọ

A na-akpọ trapezoid, nke akụkụ abụọ dị n'otu akụkụ ya kwụ ọtọ, a na-akpọ rectangular.

∠BAD = ∠ABC = 90°

Trapezoid dị iche iche

A trapezoid bụ scalene ma ọ bụrụ na akụkụ ya adịghị nhata na ọ dịghị nke ọ bụla n'ime isi akụkụ ziri ezi.

Njirimara trapezoidal

Njirimara ndị edepụtara n'okpuru ebe a na-emetụta ụdị trapezoid ọ bụla. A na-egosi ihe onwunwe na trapezoid na weebụsaịtị anyị n'akwụkwọ dị iche iche.

Ngwongwo 1

Nchikota akụkụ nke trapezoid dị n'akụkụ otu akụkụ bụ 180 °.

α + β = 180°

Ngwongwo 2

Midline nke trapezoid dị na ntọala ya ma hà nhata ọkara nke nchikota ha.

Ngwongwo 3

Akụkụ nke na-ejikọta etiti etiti nke diagonals nke trapezoid dị n'etiti etiti ya ma hà nhata ọkara ọdịiche nke ntọala.

• KL akụkụ ahịrị nke na-ejikọ ọnụ n'etiti diagonals AC и BD
• KL dabere na midline nke trapezium MN

Ngwongwo 4

Isi ihe nke njikọ nke diagonals nke trapezoid, mgbatị nke akụkụ ya na etiti etiti nke ntọala ahụ na-edina n'otu ahịrị kwụ ọtọ.

• DK - n'ihu n'akụkụ CD
• AK - n'ihu n'akụkụ AB
• E - n'etiti isi BCIe BE = EC
• F - n'etiti isi ADIe AF = FD

Ọ bụrụ na nchikota akụkụ n'otu ntọala bụ 90° (ntụgharị ∠DAB + ∠ADC u90d XNUMX °), nke pụtara na ndọtị nke akụkụ nke trapezoid na-agafe n'akụkụ aka nri, na akụkụ nke na-ejikọta etiti etiti nke ntọala (ML) hà nhata na ọkara nke ọdịiche ha.

Ngwongwo 5

Ihe diagonal nke trapezoid na-ekewa ya na triangles 4, abụọ n'ime ha (na ntọala), na abụọ ndị ọzọ (n'akụkụ) hà nhata.

• ΔAED ~ ΔBEC
• S_ΔABE =S_ΔCED

Ngwongwo 6

Enwere ike ịkọwa akụkụ nke na-agafe ebe nrutu nke diagonals nke trapezoid dị na ntọala ya n'usoro ogologo nke ntọala:

Ngwongwo 7

Bisector nke akụkụ trapezoid nwere otu akụkụ akụkụ ahụ na-adakọ ọnụ.

• AP - bisector ∠AJỌỌ
• BR - bisector ∠ABC
• AP n'akụkụ ọnụ BR

Ngwongwo 8

Enwere ike ịdekọ okirikiri naanị na trapezoid ma ọ bụrụ na nchikota ogologo nke ntọala ya hà nhata na nchikota ogologo nke akụkụ ya.

Ndị ahụ. AD + BC = AB + CD

Oghere okirikiri nke edere na trapezoid ruru ọkara ịdị elu ya: R = h/2.