Dab tsi yog trapezoid: txhais, hom, khoom

Hauv kev tshaj tawm no, peb yuav xav txog cov ntsiab lus, hom thiab cov khoom (hais txog kab pheeb ces kaum, lub kaum sab xis, nruab nrab, qhov sib tshuam ntawm ob sab, thiab lwm yam) ntawm ib qho ntawm cov duab geometric tseem ceeb - lub trapezoid.

Lub ntsiab lus ntawm lub trapezoid

Trapezium yog ib lub quadrilateral, ob sab uas yog parallel thiab lwm yam tsis yog.

Parallel sab hu ua lub hauv paus ntawm ib tug trapezoid (AD и BC), lwm ob sab sab (AB y CD).

Lub kaum sab xis ntawm lub hauv paus ntawm lub trapezoid - lub sab hauv ntawm lub trapezoid tsim los ntawm nws lub hauv paus thiab sab, piv txwv li, α и β.

Lub trapezoid yog sau los ntawm kev teev nws cov vertices, feem ntau yog qhov no ABCD. Thiab cov hauv paus yog qhia los ntawm cov ntawv Latin me me, piv txwv li, a и b.

Txoj kab nruab nrab ntawm lub trapezoid (MN) - ib ntu txuas cov midpoints ntawm nws sab sab.

Trapeze Qhov siab (h or BK) yog ib qho perpendicular kos los ntawm ib lub hauv paus mus rau lwm qhov.

Hom ntawm trapezium

Isosceles trapezoid

Lub trapezoid uas nws sab sib npaug yog hu ua isosceles (los yog isosceles).

AB = CD

Daim duab trapezium

Ib tug trapezoid, nyob rau hauv uas ob lub ces kaum ntawm ib qho ntawm nws lateral sab yog ncaj, yog hu ua rectangular.

∠BAD = ∠ABC = 90°

Ntau yam trapezoid

Lub trapezoid yog scalene yog tias nws ob sab tsis sib npaug thiab tsis muaj lub hauv paus kaum sab xis.

Trapezoidal Properties

Cov khoom uas tau teev tseg hauv qab no siv rau txhua hom trapezoid. Cov cuab yeej thiab trapezoids tau nthuav tawm ntawm peb lub vev xaib hauv kev tshaj tawm cais.

Khoom Muaj Khoom 1

Qhov sib npaug ntawm cov ces kaum ntawm lub trapezoid uas nyob ib sab yog 180 °.

AB = 180°

Khoom Muaj Khoom 2

Qhov nruab nrab ntawm lub trapezoid yog sib npaug rau nws cov hauv paus thiab sib npaug ib nrab ntawm lawv cov nyiaj.

Khoom Muaj Khoom 3

Cov ntu uas txuas rau nruab nrab ntawm cov kab pheeb ces kaum ntawm lub trapezoid yog nyob ntawm nws qhov nruab nrab thiab sib npaug rau ib nrab ntawm qhov sib txawv ntawm cov hauv paus.

• KL ib kab ntu uas koom nrog cov midpoints ntawm diagonals AC и BD
• KL nyob rau hauv nruab nrab ntawm lub trapezium MN

Khoom Muaj Khoom 4

Cov ntsiab lus ntawm kev sib tshuam ntawm kab pheeb ces kaum ntawm lub trapezoid, qhov txuas ntxiv ntawm nws sab thiab nruab nrab ntawm cov hauv paus yog nyob ntawm tib txoj kab ncaj nraim.

• DK - txuas ntxiv ntawm sab CD
• AK - txuas ntxiv ntawm sab AB
• E - nruab nrab ntawm lub hauv paus BCIe PEB = EC
• F - nruab nrab ntawm lub hauv paus ADIe AB = FD

Yog hais tias qhov sum ntawm cov ces kaum ntawm ib lub hauv paus yog 90 ° (ie ∠DAB + ∠ADC u90d XNUMX °), uas txhais tau hais tias qhov txuas ntxiv ntawm ob sab ntawm lub trapezoid sib tshuam ntawm lub kaum sab xis, thiab ntu uas txuas rau nruab nrab ntawm cov hauv paus (ML) yog sib npaug rau ib nrab ntawm lawv qhov sib txawv.

Khoom Muaj Khoom 5

Cov kab pheeb ces kaum ntawm lub trapezoid faib rau hauv 4 daim duab peb sab, ob qho tib si (ntawm lub hauv paus), thiab ob sab (ntawm sab) sib npaug hauv .

• ΔAED ~ ΔBEC
• S_{Δ AB} =S_{Δ CED}

Khoom Muaj Khoom 6

Ib ntu dhau los ntawm qhov kev sib tshuam ntawm cov kab pheeb ces kaum ntawm lub trapezoid thaum uas tig mus rau nws cov hauv paus tuaj yeem qhia tau hais txog qhov ntev ntawm cov hauv paus:

Khoom Muaj Khoom 7

Lub bisectors ntawm lub kaum sab xis ntawm ib tug trapezoid nrog tib sab sab yog kev sib nrig sib perpendicular.

• AP - bisector ∠BAD
• BR - bisector ∠ABC
• AP txiav tawm BR

Khoom Muaj Khoom 8

Lub voj voog tsuas tuaj yeem sau rau hauv lub trapezoid yog tias qhov sib npaug ntawm qhov ntev ntawm nws cov hauv paus yog sib npaug rau cov lej ntawm qhov ntev ntawm nws sab.

Cov. AD + BC = AB + CD

Lub vojvoog ntawm lub voj voog inscribed nyob rau hauv lub trapezoid yog sib npaug rau ib nrab ntawm nws qhov siab: R = h/2.