Vrste paralelograma
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Transcript of Vrste paralelograma
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Obnovimo:
PARALELOGRAM JE ČETVOROUGAOČIJE SU NASPRAMNE STRANICE PARALELNE
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Uglovi?
α β
γδ
+ = 180o
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Dijagonale?
Polove se!
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Dakle:
Naspramne stranice: Jednake i paralelne!
Uglovi: naspramni jednaki susedni su suplementniDijagonale: polove se
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PRAVOUGAONIK KVADRAT
ROMB
VRSTE
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Pravougaonik je paralelogramčiji su svi uglovi pravi
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KOJE OSOBINE IMA PRAVOUGAONIK KAO PARALELOGRAM?
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Da li još nešto možeš zaključiti o dijagonalama?
A B
CD
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Dijagonale pravougaonika su jednake i polove se!Da li se u pravougaonik možeupisati kružnica?
NE!
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A opisati?
Može!
o
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Koliko osa simetrije ima pravougaonik?
Dve!
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PRAVOUGAONIK:Stranice: naspramne jednake i paralelneUglovi: svi praviDijagonale: jednake i polove seOse simetrije: 2
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Zadaci: 1.Dijagonala pravougaonika gradi sakraćom stranicom ugao od 54o. Koliki
ugao gradi sa dužom stranicom?2. Dijagonale pravougaonika obrazujuugao od 130o. Izračunaj uglove kojedijagonale grade sa stranicama pravougaonika.
Domaći: 4.43. 4.44. 4.45.
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KVADRAT JE PRAVOUGAONIK ČIJE SUSVE STRANICE JEDNAKE.
Ako je pravougaonik, koje osobine ima?
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Dijagonale kvadrata su uzajamnonormalne!
A B
CD
O
45O
9OO
==
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KOLIKO OSA SIMETRIJE IMAKVADRAT?
4!
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DA LI SE OKO KVADRATA MOŽEOPISATI KRUŽNICA?A UPISATI?
O
GDE SU IM CENTRI?
NACRTAJ KVADRAT PA OKO NJEGA OPIŠI I U NJEGA UPIŠI KRUŽNICU.
R
r
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KVADRAT:Stranice: naspramne paralelne, a sve četiri jednakeUglovi: svi praviDijagonale: jednake, polove se uzajamno normalne, simetrale uglovaOse simetrije: 4
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Domaći zadatak:1.Konstruiši pravougaonik stranica 4cm i 6cm i opisanu kružnicu.
2.Konstruiši kvadrat stranice4cm i oko njega opiši i u njegaupiši kružnicu.
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Romb je paralelogram sajednakim stranicama.
a
a
a
a
Osobine?
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Dakle:
Naspramne stranice: Jednake i paralelne!
Uglovi: naspramni jednaki susedni su suplementniDijagonale: polove se
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Dijagonale romba seku sepod pravim uglom.
a
a
a
a
Dokažim
o!
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Podsetimo se!
A B
simet
rala
C
= ==
=
D
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a
a
a
a
A B
CD
BA=BCDA=DC
DB je simetrala duži AC, pa je DB normala na AC.
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Jedna dijagonala je simetrala druge.Dijagonale romba su simetrale unutrašnjih uglova!Zato se u romb može upisati kružnica.Dijagonale romba su njegoveose simetrije.
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O
h r=h:2
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Koje zajedničke osobine imaju kvadrat i romb?
Normalne dijagonale!
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1.U rombu je jedna dijagonala jednaka stranici. Odredi uglovetog romba.2.Obim romba je 24cm, a visina 3cm.Odredi uglove tog romba.3.U rombu visina i dijagonala, povučene iz istog temena, obrazuju ugao od 15o. Izračunati unutrašnjeuglove romba.D.Z. 4.52. 4.53. 4.55.