txheem
Hauv kev tshaj tawm no, peb yuav txiav txim siab txog cov ntsiab lus thiab cov khoom tseem ceeb ntawm cov kab nruab nrab ntawm lub convex quadrilateral txog lawv qhov kev sib tshuam, kev sib raug zoo nrog kab pheeb ces kaum, thiab lwm yam.
Nco ntsoov: Hauv cov hauv qab no, peb yuav txiav txim siab tsuas yog daim duab convex.
Kev txiav txim siab ntawm qhov nruab nrab ntawm ib lub quadrilateral
Cov ntu txuas cov midpoints ntawm lub opposite sab ntawm lub quadrilateral (xws li tsis intersecting lawv) yog hu ua nws kab nruab nrab.
- EF - kab nruab nrab txuas cov midpoints AB и CD; AE = EB, CF = FD.
- GH - kab nruab nrab cais cov midpoints BC и AD; BG = GC, AH = HD.
Properties ntawm midline ntawm ib tug quadrilateral
Khoom Muaj Khoom 1
Cov kab nruab nrab ntawm lub quadrilateral intersect thiab bisect ntawm qhov chaw ntawm kev sib tshuam.
- EF и GH (cov kab nruab nrab) sib tshuam ntawm ib qho chaw O;
- EO = OB, GO = OH.
Nco ntsoov: Point O is nruab nrab (los yog barycenter) quadrilateral.
Khoom Muaj Khoom 2
Lub ntsiab lus ntawm kev sib tshuam ntawm cov midlines ntawm lub quadrilateral yog qhov nruab nrab ntawm cov ntu txuas cov midpoints ntawm nws cov kab pheeb ces kaum.
- K - nruab nrab ntawm kab pheeb ces kaum AC;
- L - nruab nrab ntawm kab pheeb ces kaum BD;
- KL hla ib qho taw tes O, txuas K и L.
Khoom Muaj Khoom 3
Lub midpoints ntawm ob sab ntawm ib lub quadrilateral yog cov vertices ntawm parallelogram hu ua Parallelogram ntawm Varignon.
Qhov chaw ntawm lub parallelogram tsim nyob rau hauv no txoj kev thiab lub ntsiab lus ntawm kev sib tshuam ntawm nws cov kab pheeb ces kaum yog lub midpoint ntawm lub midlines ntawm tus thawj quadrilateral, piv txwv li lawv taw tes ntawm kev sib tshuam. O.
Nco ntsoov: Lub cheeb tsam ntawm ib qho parallelogram yog ib nrab ntawm thaj tsam ntawm lub quadrilateral.
Khoom Muaj Khoom 4
Yog hais tias lub kaum sab xis ntawm cov kab pheeb ces kaum ntawm lub quadrilateral thiab nws cov midline yog sib npaug, ces cov diagonals muaj qhov ntev.
- EF - kab nruab nrab;
- AC и BD - kab pheeb ces kaum;
- ∠ ELC = ∠BMF = a, Yog li ntawd AB = BD.
Khoom Muaj Khoom 5
Lub midline ntawm ib lub quadrilateral yog tsawg dua los yog sib npaug rau ib nrab ntawm nws cov uas tsis yog kev sib tshuam sab (muab hais tias cov sab no yog parallel).
EF - kab nruab nrab uas tsis cuam tshuam nrog ob sab AD и BC.
Hauv lwm lo lus, qhov nruab nrab ntawm lub plaub fab yog sib npaug rau ib nrab ntawm cov nyiaj ntawm sab uas tsis cuam tshuam nws yog tias thiab tsuas yog qhov muab plaub ntug yog lub trapezoid. Hauv qhov no, cov kev txiav txim siab sab yog cov hauv paus ntawm daim duab.
Khoom Muaj Khoom 6
Rau lub midline vector ntawm ib qho arbitrary quadrilateral, cov nram qab no sib npaug:
