Okuqukethwe
Kulolu shicilelo, sizocubungula incazelo, izinhlobo kanye nezakhiwo (ngokuphathelene nama-diagonal, ama-engeli, umugqa ophakathi, iphuzu lokuhlangana kwezinhlangothi, njll.) kwesinye sezimo zejometri eziyinhloko - i-trapezoid.
Incazelo ye-trapezoid
ITrapezium i-quadrilateral, izinhlangothi ezimbili zazo ezihambisanayo kanti ezinye ezimbili azifani.
Izinhlangothi ezihambisanayo zibizwa izisekelo ze-trapezoid (AD и BC), ezinye izinhlangothi ezimbili side (AB kanye ne-CD).
I-engeli phansi kwe-trapezoid - i-angle yangaphakathi ye-trapezoid eyakhiwe isisekelo sayo nohlangothi, isibonelo, α и β.
I-trapezoid ibhalwa ngokufaka ohlwini ama-vertices ayo, ngokuvamile lokhu A B C D. Futhi izisekelo ziboniswa ngezinhlamvu ezincane zesiLatini, isibonelo, a и b.
Umugqa omaphakathi we-trapezoid (MN) – ingxenye exhumanisa amaphoyinti amaphakathi ezinhlangothi zayo ezisemaceleni.
Ukuphakama kweTrapeze (h or BK) iyi-perpendicular edwetshiwe isuka kwesinye isisekelo iye kwesinye.
Izinhlobo ze-trapezium
Isosceles trapezoid
I-trapezoid izinhlangothi zayo ezilinganayo ibizwa ngokuthi isosceles (noma isosceles).
AB = CD
I-trapezium engunxande
I-trapezoid, lapho womabili ama-engeli kwelinye lezinhlangothi zayo ezingemuva eqondile, ibizwa ngokuthi unxande.
∠BAD = ∠ABC = 90°
I-trapezoid ehlukahlukene
I-trapezoid i-scalene uma izinhlangothi zayo zingalingani futhi awekho ama-engeli ayisisekelo alungile.
Izakhiwo ze-Trapezoidal
Izakhiwo ezibalwe ngezansi zisebenza kunoma yiluphi uhlobo lwe-trapezoid. Izakhiwo kanye nama-trapezoid ethulwa kuwebhusayithi yethu ezincwadini ezihlukene.
Impahla 1
Isamba sama-engeli e-trapezoid asondelene nohlangothi olufanayo ngu-180°.
α + β = 180°
Impahla 2
Umugqa omaphakathi we-trapezoid uhambisana nezisekelo zawo futhi ulingana nohhafu wesamba sazo.
Impahla 3
Ingxenye ehlanganisa amaphoyinti amaphakathi we-diagonals ye-trapezoid ilele kumugqa wayo omaphakathi futhi ilingana nohhafu womehluko wezisekelo.
- KL ingxenye yomugqa ejoyina amaphoyinti amaphakathi wamadiagonali AC и BD
- KL ilele emgqeni omaphakathi we-trapezium MN
Impahla 4
Amaphuzu okuphambana kwe-diagonal ye-trapezoid, izandiso zezinhlangothi zayo kanye namaphoyinti aphakathi kwezisekelo alele emgqeni ofanayo oqondile.
- DK – ukuqhubeka kohlangothi CD
- AK – ukuqhubeka kohlangothi AB
- E – maphakathi nesisekelo BCIe BE = EC
- F – maphakathi nesisekelo ADIe AF = FD
Uma isamba sama-engeli esisekelweni esisodwa singama-90° (okungukuthi ∠DAB + ∠ADC u90d XNUMX °), okusho ukuthi izandiso zezinhlangothi ze-trapezoid ziphambana nge-engeli engakwesokudla, kanye nengxenye exhumanisa amaphoyinti aphakathi kwezisekelo (ML) ilingana nengxenye yomehluko wabo.
Impahla 5
I-diagonals ye-trapezoid ihlukanisa ibe ngonxantathu abangu-4, ababili babo (ezisekelweni), kanti abanye ababili (emaceleni) balingana ngo-.
- ΔAED ~ ΔBEC
- SΔABE =SΔCED
Impahla 6
Isegimenti edlula endaweni yokuhlangana yama-diagonal we-trapezoid ehambisana nezisekelo zayo ingavezwa ngokuya ngobude bezisekelo:
Impahla 7
Ama-engeli amabili e-trapezoid anohlangothi olufanayo olusemaceleni ancikene.
- AP – i-bisector ∠BAD
- BR – i-bisector ∠ABC
- AP i-perpendicular BR
Impahla 8
Umbuthano ungabhalwa kuphela ku-trapezoid uma isamba sobude bezisekelo zawo silingana nesamba sobude bezinhlangothi zawo.
Labo. AD + BC = AB + CD
Irediyasi yombuthano ebhalwe ku-trapezoid ilingana nengxenye yobude bayo: R = h/2.