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A cikin wannan ɗaba'ar, za mu yi la'akari da ma'ana da manyan kaddarorin tsakiyar layi na maɗaukakiyar ɗimbin ɗabi'a game da mahaɗinsu, alaƙa da diagonal, da sauransu.
lura: A cikin abin da ke biyo baya, za mu yi la'akari da adadi mai ma'ana kawai.
Ƙaddamar da tsakiyar layi na hudu
Bangaren da ke haɗa tsaka-tsaki na ɓangarorin gaba dayan hudu (watau ba tare da su ba) ana kiransa da shi. layin tsakiya.
- EF - layin tsakiya yana haɗa tsaka-tsaki AB и CD; AE=EB, CF=FD.
- GH – Tsakanin layi mai raba tsaka-tsaki BC и AD; BG=GC, AH=HD.
Halayen tsakiyar layi na huɗu
Kadarori 1
Layukan tsakiya na tsaka-tsakin tsaka-tsaki da kuma bisect a wurin tsaka-tsakin.
- EF и GH (layi na tsakiya) suna tsaka-tsaki a wuri guda O;
- EO = OF, GO=OH.
lura: Point O is centroid (ko barrycenter) hudu.
Kadarori 2
Matsakaicin tsaka-tsakin tsaka-tsakin tsaka-tsakin huɗun shine tsakiyar tsakiya na ɓangaren da ke haɗa tsakiyar tsakiyar diagonals.
- K – tsakiyar diagonal AC;
- L – tsakiyar diagonal BD;
- KL ya wuce ta aya O, haɗawa K и L.
Kadarori 3
Matsakaicin ɓangarorin ma'auni huɗun su ne ƙarshen layi ɗaya da ake kira Parallelogram na Varignon.
Wurin daidaitawar da aka samu ta wannan hanya kuma wurin mahadar diagonal ɗinsa ita ce tsakiyar tsakiyar layi na asali huɗun, watau wurin mahaɗarsu. O.
lura: Yankin layi daya shine rabin yanki na yanki mai hudu.
Kadarori 4
Idan kusurwoyin da ke tsakanin diagonal na ma'auni na huɗu da tsakiyar layinsa daidai suke, to, diagonal ɗin suna da tsayi iri ɗaya.
- EF - layin tsakiya;
- AC и BD - diagonal;
- ∠ELC = ∠BMF = a, Sakamakon haka AC=BD.
Kadarori 5
Matsakaicin layin huɗu bai kai ko dai-dai da rabin jimlar ɓangarorinsa waɗanda ba su haɗa su ba (idan har waɗannan bangarorin sun yi daidai da juna).
EF - layin tsaka-tsaki wanda ba ya haɗuwa da tarnaƙi AD и BC.
A wasu kalmomi, tsakiyar layi na quadrilateral yana daidai da rabin jimlar sassan da ba su haɗa shi ba idan kuma kawai idan an ba da ita ta hanyar trapezoid. A wannan yanayin, bangarorin da aka yi la'akari sune tushe na adadi.
Kadarori 6
Ga madaidaicin layi na tsaka-tsakin tsaka-tsaki na sabani, daidaito mai zuwa yana riƙe:
