Mukati
Muchinyorwa chino, tichatarisa tsanangudzo, marudzi uye zvivakwa (zvichienderana nediagonal, makona, midline, mharadzano yemativi, nezvimwewo) zveimwe yemhando huru dzejometri - trapezoid.
Tsanangudzo ye trapezoid
Trapezium is a quadrilateral, mativi maviri ayo akafanana uye mamwe maviri haana.
Mativi akaenzana anonzi nheyo dze trapezoid (AD и (BC), mamwe mativi maviri divi (AB uye CD).
Angle pazasi pe trapezoid - iyo yemukati kona ye trapezoid inoumbwa nenheyo yayo uye parutivi, semuenzaniso, α и β.
A trapezoid inonyorwa nekunyora vertices yayo, kazhinji izvi ndizvo ABCD. Uye zvigadziko zvinoratidzwa nemavara madiki echiLatin, semuenzaniso, a и b.
Mutsara weMedhiya we trapezoid (MN) - chikamu chinobatanidza midpoints ye lateral mativi ayo.
Trapeze Height (h or BK) is a perpendicular inotorwa kubva kune imwe nheyo kuenda kune imwe.
Mhando dze trapezium
Isosceles trapezoid
Trapezoid ine mativi akaenzana inonzi isosceles (kana isosceles).
AB = CD
Rectangular trapezium
A trapezoid, umo makona ese ari maviri kune rimwe lateral mativi akatwasuka, inonzi rectangular.
∠BAD = ∠ABC = 90°
Trapezoid yakasiyana-siyana
A trapezoid is scalene kana mativi ayo asina kuenzana uye hapana imwe yemakona epasi yakarurama.
Trapezoidal Properties
Izvo zvivakwa zvakanyorwa pazasi zvinoshanda kune chero mhando ye trapezoid. Zvivakwa uye trapezoid zvinoratidzwa pawebhusaiti yedu mumabhuku akasiyana.
Chivakwa 1
Huwandu hwemakona e trapezoid yakatarisana nedivi rimwe chete i180°.
α + β = 180°
Chivakwa 2
Mutsetse wepakati we trapezoid unofanana nezvigadziko zvawo uye wakaenzana nehafu yehuwandu hwawo.
Chivakwa 3
Chikamu chinobatanidza midpoints ye diagonals ye trapezoid inorara pakati payo uye yakaenzana nehafu yemusiyano wezvigadziko.
- KL chikamu chemutsara chinobatana pakati pemadiagonals AC и BD
- KL iri pakati petrapezium MN
Chivakwa 4
Mapoinzi ekupindirana kweiyo diagonals ye trapezoid, iyo yakawedzera mativi ayo uye midpoints yezvigadziko zvinorara pamutsara wakatwasuka.
- DK - kuenderera mberi kwedivi CD
- AK - kuenderera mberi kwedivi AB
- E - pakati pechigadziko BCIe BE = EC
- F - pakati pechigadziko ADIe AF = FD
Kana huwandu hwemakona pane imwe hwaro huri 90° (kureva ∠DAB + ∠ADC u90d XNUMX °), zvinoreva kuti kuwedzeredzwa kwemativi e trapezoid kunopindirana pakona chaiyo, uye chikamu chinobatanidza midpoints yezvigadziko.ML) yakaenzana nehafu yemusiyano wavo.
Chivakwa 5
Iyo diagonals ye trapezoid inokamura kuita 4 makona, maviri ayo (pazvigadziko), uye mamwe maviri (kumativi) akaenzana mu.
- ΔAED ~ ΔBEC
- SΔABE =SΔCED
Chivakwa 6
Chikamu chinopfuura nepamharadzano poindi yemadiagonals e trapezoid parallel kune zvigadziko zvayo inogona kuratidzwa maererano nehurefu hwemabhesi:
Chivakwa 7
Iyo bisectors yemakona e trapezoid ine imwechete lateral side inopindirana perpendicular.
- AP – bisector ∠BAD
- BR – bisector ∠ABC
- AP perpendicular BR
Chivakwa 8
Denderedzwa rinogona kunyorwa chete mu trapezoid kana huwandu hwehurefu hwezvigadziko zvahwo hwakaenzana nehuwandu hwehurefu hwemativi ayo.
Avo. AD + BC = AB + CD
Iyo radius yedenderedzwa yakanyorwa mu trapezoid yakaenzana nehafu yehurefu hwayo: R = h/2.