podudarnost trouglova
DESCRIPTION
Podudarnost trouglova, geometrijaTRANSCRIPT
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Podudarnost trouglova
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Kada govorimo o podudarnim trouglovima, mislimo da je sve u vezi njih je podudarno. Sve 3 para odgovarajućih uglova su jednaki ....
I sva 3 para odgovarajućih strana su jednaki
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Da dokažemo da su 2 osobe su identični blizanci, ne treba da pokažemo da su svih "2000" delova tela jednaki. Možemo prečicom pokazati 3 ili 4 stvari koje su jednake, kao što su njihova lica, starosti i visine. Ako su isti mislim da se možemo složiti da su blizanci. Isto važi i za trouglove. Mi ne treba da dokažemo da su svih 6 odgovarajućih delova podudarni. Imamo 4 kratke metode.
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SSSAko možemo pokazati da su sva
3 para stranica podudarni, trouglovi moraju biti
podudarni.
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SuSAko su 2 para strana i ugao izmedju njih podudarni i trouglovi moraju biti
podudarni
Uključeni ugao
Neuključeni uglovi
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Ovo se zove zajednička strana. To je strana zajednička za oba trougla.
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zadatak
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Zajednička stranicaSSS
Zajednička stranica
Unakrsni uglovi
SUS
SUS
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Drugi deo
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USU – zajednička 2 ugla I stranica izmedju njih
U
SU
SSU – Zajedničke su po 2 stranice i ugao naspram vecih stranica U
U
SSS
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SSU USU
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A C
D
Dato :AB = BDEB = BCDokaz : ∆ ABE ˜ ∆DBC
=
B
E
1 2
SUS
AB = BD Dato 1 = 2 Unakrsni ugloviEB = BC Dato∆ABE ˜ ∆DBC SUS=
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A B
C
1 2dato: CX deli ACB A ˜ Bdokaz: ∆ACX ˜ ∆BCX
X
==
USU
CX DELI ACB DATO 1 = 2 DEF A = B DATO CX = CX ZAJEDNICKA STRANICA
∆ACX ˜ ∆BCX USU=
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Dokazi da su dva trougla podudarna
A B
D C
X
DATO: AB ll DCX SREDISTE ACDOKAZ : AXB ˜ CXD=
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A
B
C
DE
1 2
DATO :AB = BD EB = BCDOKAZ : ∆ABE ˜ ∆DBC
=
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A B
D C
X
DATO: AB ll DCX SREDISTE ACDOKAZ : AXB ˜ CXD=