Kodi mzere wapakati wa quadrilateral ndi chiyani

M'bukuli, tiwona tanthauzo ndi zomwe zili mumizere yapakati pa ma convex quadrilateral ponena za mphambano yawo, ubale ndi ma diagonal, ndi zina zambiri.

Zindikirani: Zotsatirazi, tingowona chithunzi cha convex.

Timasangalala

Kutsimikiza kwa mzere wapakati wa quadrilateral

Gawo lomwe limalumikiza mapakati a mbali zotsutsana za quadrilateral (mwachitsanzo, osadutsana) limatchedwa mzere wapakati.

Kodi mzere wapakati wa quadrilateral ndi chiyani

  • EF - mzere wapakati wolumikiza nsonga zapakati AB и CD; AE=EB, CF=FD.
  • GH - mzere wapakatikati wolekanitsa ma midpoints BC и AD; BG=GC, AH=HD.

Makhalidwe apakati pa quadrilateral

Katundu 1

Mizere yapakati ya quadrilateral intersect ndi kudumpha pakati pa mphambano.

Kodi mzere wapakati wa quadrilateral ndi chiyani

  • EF и GH (mizere yapakati) kudumphadumpha pa mfundo O;
  • EO=YA, PITA=OH.

Zindikirani: Point O is pakati (kapena barycenter) quadrilateral.

Katundu 2

Malo omwe amadutsa pakati pa quadrilateral ndi pakati pa gawo lomwe limagwirizanitsa ma diagonals ake.

Kodi mzere wapakati wa quadrilateral ndi chiyani

  • K - m'katikati mwa diagonal AC;
  • L - m'katikati mwa diagonal BD;
  • KL amadutsa mfundo O, kulumikizana K и L.

Katundu 3

Pakatikati mwa mbali za quadrilateral ndi ma vertices a parallelogram yotchedwa Parallelogram ya Varignon.

Kodi mzere wapakati wa quadrilateral ndi chiyani

Pakatikati pa parallelogram yomwe idapangidwa motere komanso malo ophatikizira ma diagonals ake ndi pakatikati pa mizere yapakati ya quadrilateral yoyambirira, mwachitsanzo, podutsana. O.

Zindikirani: Dera la paralelogalamu ndi theka la gawo la quadrilateral.

Katundu 4

Ngati ngodya pakati pa ma diagonal a quadrilateral ndi midline yake ndi yofanana, ndiye kuti ma diagonal ali ndi kutalika kofanana.

Kodi mzere wapakati wa quadrilateral ndi chiyani

  • EF - mzere wapakati;
  • AC и BD - ma diagonal;
  • ∠ELC = ∠BMF = a, Chifukwa chake AC = BD. 

Katundu 5

Mzere wapakati wa quadrilateral ndi wocheperako kapena wofanana ndi theka la kuchuluka kwa mbali zake zosadutsana (malinga ngati mbalizi zikufanana).

Kodi mzere wapakati wa quadrilateral ndi chiyani

EF - mzere wapakati womwe sumadutsana ndi mbali AD и BC.

Mwa kuyankhula kwina, mzere wapakati wa quadrilateral ndi wofanana ndi theka la chiwerengero cha mbali zomwe sizimadutsana ngati ndipo pokhapokha ngati gawo la quadrilateral ndi trapezoid. Pankhaniyi, mbali zomwe zimaganiziridwa ndizo maziko a chiwerengerocho.

Katundu 6

Kwa vekita yapakati ya quadrilateral, zofanana zotsatirazi zimakhala:

Kodi mzere wapakati wa quadrilateral ndi chiyani

Kodi mzere wapakati wa quadrilateral ndi chiyani

Siyani Mumakonda