Mukati
Muchinyorwa chino, isu tichatarisa tsananguro uye huru zvimiro zvepakati peiyo convex quadrilateral maererano nenzvimbo yavo yemharadzano, hukama nemadiagonals, nezvimwe.
Cherechedza: Mune zvinotevera, isu tichatarisa chete mufananidzo weconvex.
Kutsunga kwepakati pe quadrilateral
Chikamu chinobatanidza mativi epakati pemativi akapesana e quadrilateral (kureva kusapindirana nawo) chinonzi mutsetse wepakati.
- EF - mutsara wepakati unobatanidza midpoints AB и CD; AE=EB, CF=FD.
- GH - mutsara wepakati unoparadzanisa midpoints BC и AD; BG=GC, AH=HD.
Zvivakwa zvepakati pe quadrilateral
Chivakwa 1
Mitsetse yepakati ye quadrilateral intersect uye bisect papoint of intersection.
- EF и GH (mitsetse yepakati) yambuka pane imwe nzvimbo O;
- EO=ZVE, ENDA=OH.
Cherechedza: nguva O is centroid (kana barycenter) quadrilateral.
Chivakwa 2
Nzvimbo yekupindirana kwepakati peiyo quadrilateral ndiyo yepakati pechikamu chinobatanidza midpoints yemadiagonals ayo.
- K - pakati pe diagonal AC;
- L - pakati pe diagonal BD;
- KL inopfuura nepapoindi O, kubatana K и L.
Chivakwa 3
Nzvimbo dzepakati dzemativi e quadrilateral ndiwo ma vertices eparalelogiramu inonzi Parallelogram yeVarignon.
Pakati peparalelogiramu yakaumbwa nenzira iyi uye poindi yemharadzano yemadiagonals ndiyo yepakati pemitsetse yepakutanga quadrilateral, kureva nzvimbo yavo yemharadzano. O.
Cherechedza: Nzvimbo yeparallelogram ihafu yenzvimbo ye quadrilateral.
Chivakwa 4
Kana ma angles ari pakati pe diagonals ye quadrilateral uye midline yayo yakaenzana, ipapo diagonals ine urefu hwakafanana.
- EF - mutsetse wepakati;
- AC и BD - diagonals;
- ∠ELC = ∠BMF = a, Naizvozvo AC=BD.
Chivakwa 5
Mutsetse wepakati we quadrilateral ishoma pane kana kuenzana nehafu yehuwandu hwemativi ayo asina kupindirana (chero bedzi mativi aya anoenderana).
EF - mutsara wepakati usingapesani nemativi AD и BC.
Nemamwe manzwi, mutsetse wepakati we quadrilateral wakaenzana nehafu yehuwandu hwemativi asingapindire kana uye chete kana yakapihwa quadrilateral iri trapezoid. Muchiitiko ichi, mativi anofungidzirwa ndiwo mabhesi emufananidzo.
Chivakwa 6
Kune iyo midline vector ye arbitrary quadrilateral, kuenzana kunotevera kunobata:
