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> Zadatak za jednakokrakim trouglom

jeele
post Jan 13 2007, 09:58 AM
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imam ja pitanje...
jest' glupo, ali ja ne vidim kako se ovo resava...sta, dopunjavam nesto, i onda dokazem podudarnost. samo sto mi ne ide u glavu kako da dokazem ono sto se trazi...

jednakokraki trougao ABC, uglovi na osnovicama su 40*, simetrala iz ugla CAB sece krak CB u tacki D
dokazati AD + CD = AB

This post has been edited by jeele: Jan 13 2007, 05:02 PM


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jeele
post Jan 13 2007, 01:15 PM
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inatce, ovo je za shesti... blush.gif


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Puzzler
post Jan 13 2007, 05:00 PM
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QUOTE(jeele @ Jan 13 2007, 09:58 AM)
jednakostranicni trougao ABC, uglovi na osnovicama su 40*
*



Jednakostranični? 40*? blink.gif blink.gif blink.gif

biggrin.gif

Mada, shvatio sam šta želiš da kažeš...

A rešenje?
Pa, nisam još uradio XD.gif


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jeele
post Jan 13 2007, 05:01 PM
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jednakokraki...
katastrofa... sad.gif sad.gif wacko.gif unsure.gif blush.gif

This post has been edited by jeele: Jan 13 2007, 05:03 PM


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Puzzler
post Jan 13 2007, 05:48 PM
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Izaberimo tačku E tako da važi AC=AF i B( A,E,B ).

Pošto je
AC=AE
AD=AD
<EAD=<DAC (prema usl. zadatka)

tada, prema SUS, sledi da su ova dva trougla, AED i ACD, podudarna.
Iz podudarnosti sledi CD=ED(*), <AED=<ACD.
Pošto je <ACD=100* (iz uslova zadatka), tada je i <AED=100*, pa je <BED=80*.


Izaberimo tačku F tako da je BF=FD(**) i B( B,F,A ).
Pošto je <FBD=40* (prema uslovu zadatka), tad je i ugao <FBD=40*, pa je ugao <BFD=100*, a samim tim <AFD=80*.

Pošto je <EFD=<FED=80*, zaključujemo ED=FD(***).

Iz (*),(**) i (***) sledi CD=FB.

Pošto su uglovi na osnovici trougla EFD jednaki 80, onda je <EDF=20*.
<ADF=<ADE+<EDF=60*+20*=80*

<AFD=80*

Iz ovoga sledi AF=AD.

Pošto je

AF=AD
FB=CD \ \ \ \ \ \ \ \ \ \ \ \ => AD+CD=AB
AF+FB=AB


Nadam se da je dovoljno. wink.gif

This post has been edited by Puzzler: Jan 13 2007, 05:50 PM


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jeele
post Jan 13 2007, 05:52 PM
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a hA!
thanx thanx blush.gif blush.gif blush.gif
me so stupid... :smajli koji se krije...:


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Puzzler
post Jan 13 2007, 05:52 PM
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Ma nisi, i meni je trebalo poprilično... XD.gif


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Laza_91
post Jan 14 2007, 03:05 PM
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Čime se vi bavite blink.gif
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Anchi
post Jan 14 2007, 04:16 PM
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A cime bi trebalo?
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Laza_91
post Jan 14 2007, 10:41 PM
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Pa raspust je...
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Anchi
post Jan 14 2007, 11:40 PM
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Pa jeste.... Mada.... Kada se vratimo, za prve dve- najvise tri nedelje imamo : pismeni iz geometrije, kontrolni iz geometrije (vektori), zajednicki pismeni iz geometrije, pismeni iz fizike..... Strasno! (to je ono sto je vec najavljeno, bice ih verovatno jos...)
Jos samo nedelju dana... Smrc! sad.gif crybaby.gif ohmy.gif

This post has been edited by Anchi: Jan 14 2007, 11:41 PM
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Laza_91
post Jan 15 2007, 12:29 PM
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da,da,da, u pravu si...A nisam ni 1/3 zadataka uradio...
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Anchi
post Jan 15 2007, 01:47 PM
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Ma nisam ni ja sve... Mrzelo me mnogo da ucim..
Prvu polovinu raspusta provela sam (uglavnom) igrajuci Need for speed biggrin.gif biggrin.gif biggrin.gif
Sada moram sve to da ucim!!! mad.gif crybaby.gif
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Puzzler
post Jan 15 2007, 05:39 PM
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Ja ispadoh štreber po običaju...
Uradio sam svih onih 70 zadataka što nam je ljubazno zadala razredna... rolleyes.gif
I još vežbao fiziku za takmičenja...

*goin' to kill myself*


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Laza_91
post Jan 15 2007, 06:05 PM
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I očekivali smo da ćeš ti sve da uradiš+dodatno...

Šta imamo za lektiru iz srpskog???
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Puzzler
post Jan 15 2007, 06:55 PM
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UH... Mnogo...

- Odlomci iz "Epa o Gilgamešu"
- Odlomci iz "Ilijade"

Ima još, ali ovo sam se trenutno setio...
Kad pogledam, dopisaću. wink.gif


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Iva
post Jan 15 2007, 07:56 PM
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Ne bih ni ja umela da resim zadatak.. svaka cast Puzzlere wink.gif smile.gif stvarno!!

PS Mi moramo celog Gilgamesha laugh.gif


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Puzzler
post Jan 15 2007, 09:57 PM
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Ponekad zaista volim MG...


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Anchi
post Jan 15 2007, 10:23 PM
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QUOTE
Odlomci iz "Epa o Gilgamešu"

QUOTE
Odlomci iz "Ilijade

E a za kada je to? Ne secam se kada je nama to rekla da radimo... Nije valjda da moram jos i to da citam sada.. dry.gif

A i ja sam fiziku malo vezbala za takmicenja, i malo matis... i one zadatke sto je dala vasa razredna... Samo.. Sve po malo, nisam ih jos sve zavrsila. biggrin.gif
Uostalom,
Svi matematicari su shtreberi ==> i mi smo shtreberi
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^_NiN0_^
post Jan 15 2007, 10:29 PM
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Zadatak resen ... jos jedna zakljucana tema za mene 33gc2.gif lockly0.gif


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