Mene ne trapezoid: definition, iri, kaddarorin

A cikin wannan ɗaba'ar, za mu yi la'akari da ma'anar, nau'o'in da kaddarorin (game da diagonals, kusurwa, tsakiyar layi, tsaka-tsakin tarnaƙi, da dai sauransu) na ɗaya daga cikin manyan siffofi na geometric - trapezoid.

Ma'anar trapezoid

Trapezium yanki ne na hudu, bangarorin biyu suna daidai da juna sauran biyun kuma ba haka suke ba.

Ana kiran sassan layi daya tushe na trapezoid (AD и BC), sauran bangarorin biyu gefen (AB da CD).

Angle a gindin trapezoid - kusurwar ciki na trapezoid kafa ta tushe da gefensa, misali; α и β.

Ana rubuta trapezoid ta hanyar jera madaidaitan sa, galibi wannan shine ABCD. Kuma tushen ana nuna su da ƙananan haruffan Latin, misali, a и b.

Matsakaicin layin trapezoid (MN) - wani yanki da ke haɗa tsaka-tsakin ɓangarorinsa na gefe.

Tsawon Trapeze (h or BK) shi ne madaidaicin da aka zana daga tushe zuwa wancan.

Nau'in trapezium

Isosceles trapezoid

Wani trapezoid wanda gefensa daidai yake ana kiransa isosceles (ko isosceles).

AB = CD

Trapezium rectangular

A trapezoid, wanda duka kusurwoyi a daya daga cikin gefen gefensa suna madaidaiciya, ana kiransa rectangular.

∠BAD = ∠ABC = 90°

M trapezoid

Trapezoid yana da sikelin idan sassansa ba daidai ba ne kuma babu ɗayan kusurwoyin tushe daidai.

Trapezoidal Properties

Abubuwan da aka jera a ƙasa sun shafi kowane nau'in trapezoid. Ana gabatar da Properties da trapezoid akan gidan yanar gizon mu a cikin wallafe-wallafe daban-daban.

Kadarori 1

Jimlar kusurwoyin trapezoid da ke kusa da wannan gefe shine 180 °.

α + β = 180°

Kadarori 2

Tsakanin layin trapezoid yana daidai da tushe kuma yana daidai da rabin adadin su.

Kadarori 3

Bangaren da ke haɗa tsaka-tsaki na diagonals na trapezoid ya ta'allaka ne akan tsakiyar layinsa kuma yana daidai da rabin bambancin tushe.

• KL sashin layi wanda ya haɗu da tsakiyar maki na diagonals AC и BD
• KL ya ta'allaka ne a tsakiyar layin trapezium MN

Kadarori 4

Matsakaicin tsaka-tsaki na diagonals na trapezoid, daɗaɗɗen sassansa da kuma tsaka-tsakin tushe suna kwance akan layi madaidaiciya.

• DK - ci gaba na gefe CD
• AK - ci gaba na gefe AB
• E – tsakiyar tushe BCIe BE = EC
• F – tsakiyar tushe ADIe AF = FD

Idan jimillar kusurwoyi a gindi ɗaya 90° ne (watau ∠DAB + ∠ADC u90d XNUMX °), wanda ke nufin cewa haɓakar bangarorin trapezoid sun haɗu a kusurwar dama, da kuma ɓangaren da ke haɗuwa da tsaka-tsakin tushe (ML) daidai yake da rabin bambancinsu.

Kadarori 5

Diagonal na trapezoid sun raba shi zuwa triangles 4, biyu daga cikinsu (a sansanonin), da sauran biyun (a tarnaƙi) daidai suke a cikin.

• ΔAED ~ ΔBEC
• S_ΔABE = S ba_ΔCED

Kadarori 6

Wani yanki da ke wucewa ta hanyar tsaka-tsaki na diagonal na trapezoid a layi daya da sansanoninsa ana iya bayyana shi cikin tsayin dakaru:

Kadarori 7

Bisectors na kusurwoyi na trapezoid tare da gefe ɗaya na gefe suna tsaye a kan juna.

• AP - bisector ∠ BABU
• BR - bisector ∠ABC
• AP perpendicular BR

Kadarori 8

Za a iya rubuta da'irar kawai a cikin trapezoid idan jimillar tsayin sansanoninsa ya yi daidai da jimlar tsayin sassansa.

Wadancan. AD + BC = AB + CD

Radius na da'irar da aka rubuta a cikin trapezoid daidai yake da rabin tsayinsa: R = h/2.