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# A Triangle ABC is given with 2 angles : x,y are angles lying

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A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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08 Aug 2009, 08:54
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A Triangle ABC is given with 2 angles : x,y are angles lying across AC and AB ,respectively.

Is triangle ABC isosceles?

1/ X does not equal Y
2/ AB=2BC
SVP
Joined: 05 Jul 2006
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Kudos [?]: 316 [0], given: 49

Re: A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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08 Aug 2009, 09:23
A Triangle ABC is given with 2 angles : x,y are angles lying across AC and AB ,respectively.

Is triangle ABC isosceles?

1/ X does not equal Y
2/ AB=2BC

E

each alone is not suff

both

side bc corresponds to the 3rd angle z, and as long as bc = 1/2 ab thus y>z, ie: x not = y , y not = z however we dont know the relation bet x,z.
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Kudos [?]: 475 [4] , given: 22

Re: A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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08 Aug 2009, 20:42
4
KUDOS
IMO C

Statement 1: x and y are not equal
so AB not equal to AC, But not sure about the other sides , so stmt1 insufficient

Statement 2: AB =2BC , so AB not equal to BC, but dont know about any other sides, so stmt2 insufficient

combining two statements,
AB not equal to AC,
AB not equal to BC,
so the remaining sides AC must be equal to BC for the triangle to be isoceles.
According to triangle inequality,
AC+BC must be greater than the third side AB
AC + BC > AB
AC + BC > 2BC ( given in question AB = 2BC)
AC > BC , so the triangle is not isoceles, hence the optio C.
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Joined: 05 Jul 2006
Posts: 1743
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Kudos [?]: 316 [0], given: 49

Re: A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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09 Aug 2009, 02:11
crejoc wrote:
IMO C

Statement 1: x and y are not equal
so AB not equal to AC, But not sure about the other sides , so stmt1 insufficient

Statement 2: AB =2BC , so AB not equal to BC, but dont know about any other sides, so stmt2 insufficient

combining two statements,
AB not equal to AC,
AB not equal to BC,
so the remaining sides AC must be equal to BC for the triangle to be isoceles.
According to triangle inequality,
AC+BC must be greater than the third side AB
AC + BC > AB
AC + BC > 2BC ( given in question AB = 2BC)
AC > BC , so the triangle is not isoceles, hence the optio C.

great approach , thanks...kudus
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Re: A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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14 Aug 2009, 08:26
crejoc wrote:
IMO C
According to triangle inequality,
AC+BC must be greater than the third side AB
AC + BC > AB
AC + BC > 2BC ( given in question AB = 2BC)
AC > BC , so the triangle is not isoceles, hence the optio C.

gr8 didnt think abt it..
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Re: A Triangle ABC is given with 2 angles : x,y are angles lying [#permalink]

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14 Aug 2009, 08:47
crejoc wrote:
IMO C

Statement 1: x and y are not equal
so AB not equal to AC, But not sure about the other sides , so stmt1 insufficient

Statement 2: AB =2BC , so AB not equal to BC, but dont know about any other sides, so stmt2 insufficient

combining two statements,
AB not equal to AC,
AB not equal to BC,
so the remaining sides AC must be equal to BC for the triangle to be isoceles.
According to triangle inequality,
AC+BC must be greater than the third side AB
AC + BC > AB
AC + BC > 2BC ( given in question AB = 2BC)
AC > BC , so the triangle is not isoceles, hence the optio C.

Wonderful solution!! +1
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Re: A Triangle ABC is given with 2 angles : x,y are angles lying   [#permalink] 14 Aug 2009, 08:47
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