ZNAČAJNE TAČKE TROUGLA
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Transcript of ZNAČAJNE TAČKE TROUGLA
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Begzada Kišić
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Centar opisane kružnice
Centar upisane kružnice
Težište
Ortocentar
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Opisana kružnica prolazi kroz vrhove trougla
Upisana kružnica dodiruje stranice trougla
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Neka su date dvije kružnice sa centrima O i O1
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Prvoj ćemo upisati, a drugoj opisati trougao
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Kako uraditi obrnuto?Kako datom trouglu opisati ili upisati kružnicu?
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Opisana kružnica
Vrhovi trougla A, B i C pripadaju kružnici tj. AO=BO=CO
Tačka O pripada simetralama stranica AB, BC i AC
Simetrale stranica trougla sijeku se u tački O
Dodirne tačke D, E i F pripadaju kružnici tj. DO1=EO1=FO1
Tačka O1 pripada simetralama uglova trougla
Simetrale uglova trougla sijeku se u tački O1
Upisana kružnica
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Centar kružnice opisane oko trougla je tačka u kojoj se sijeku simetrale stranica trougla
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Centar kružnice upisane u trougao je tačka u kojoj se sijeku simetrale uglova trougla
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Težište trougla je tačka u kojoj se sijeku težišnice trougla
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Ortocentar trougla je tačka u kojoj se sijeku visine trougla
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Zadaci po grupama I GRUPA: Naći centar kružnice opisane oko tupouglog trougla i konstruisati je II GRUPA: Naći centar kružnice opisane oko pravouglog trougla i konstruisati je III GRUPA: Naći centre opisane i upisane kružnice jednakostraničnog trougla i konstruisati ih IV GRUPA: Konstruisati težište tupouglog trougla V GRUPA: Konstruisati ortocentar tupouglog trougla VI GRUPA: Konstruisati ortocentar pravouglog trougla
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Imaj povjerenja u samog sebe pa ćeš uspjeti
Goethe
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Rješenje grupe I
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Rješenje grupe II
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Rješenje grupe III
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Rješenje grupe IV
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Rješenje grupe V
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Rješenje grupe VI
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Zaključci:
Kod tupouglog trougla centar opisane kružnice je van trougla
Kod pravouglog trougla centar opisane kružnice je središte hipotenuze
Kod jednakostraničnog trougla značajne tačke se poklapaju
Težište je uvijek u trouglu i svaku težišnicu dijeli u omjeru 2:1
Ortocentar tupouglog trougla je van trougla Ortocentar pravouglog trougla je tjeme kod
pravog ugla
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Kako bismo odredili centar proizvoljne kružnice?
Možemo uzeti tri tačke na kružnici i odrediti simetrale dviju tetiva
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Hvala na pažnji!