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# If two angles of a triangle are equal, is the triangle

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Director
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If two angles of a triangle are equal, is the triangle [#permalink]  30 Jul 2008, 17:14
If two angles of a triangle are equal, is the triangle isosceles???

My answer is no. Because we dont knwo the thrid angle. And if the thrid angle is same too then its an equilateral triangle.

Is that true?
Director
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Re: geometery confusion [#permalink]  30 Jul 2008, 17:21
I think answer should be yes. Even an equilateral triangle is an special case of Isoceles triangle in which third angle happens of to be same as the other two triangles.

It is the same logic as why every square is rhombus or rectangle.
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Re: geometery confusion [#permalink]  30 Jul 2008, 17:54
I don't think there's a universally accepted answer to this question in math circles. It is now normal to consider equilateral triangles as isosceles (just as squares are considered parallelograms), but that wasn't always the case- two or three hundred years ago, an isosceles triangle was normally defined to have precisely two equal sides and angles - and I'd bet there are still people who go by that definition. This is not a distinction you will ever need to know about for the GMAT, but if you're curious, the Official Guide defines an isosceles triangle as one with 'at least two equal sides', so equilateral triangles are officially isosceles on the GMAT.
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Director
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Re: geometery confusion [#permalink]  30 Jul 2008, 18:15
IanStewart wrote:
I don't think there's a universally accepted answer to this question in math circles. It is now normal to consider equilateral triangles as isosceles (just as squares are considered parallelograms), but that wasn't always the case- two or three hundred years ago, an isosceles triangle was normally defined to have precisely two equal sides and angles - and I'd bet there are still people who go by that definition. This is not a distinction you will ever need to know about for the GMAT, but if you're curious, the Official Guide defines an isosceles triangle as one with 'at least two equal sides', so equilateral triangles are officially isosceles on the GMAT.

Thanks for pointing out. Make sense now....
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Re: geometery confusion [#permalink]  30 Jul 2008, 21:03
rao_1857 wrote:
If two angles of a triangle are equal, is the triangle isosceles???

My answer is no. Because we dont knwo the thrid angle. And if the thrid angle is same too then its an equilateral triangle.

Is that true?

its an interesting but i think it is. the question is similar to is 64 a square of an integer? yes, it is. since 64 is a cube of 4, it doesnot mean that its not a square. its a square and a cube as well.

similarly all angle equal triangle is isosceles as well as equilateral trangle.
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Re: geometery confusion [#permalink]  30 Jul 2008, 21:37
interesting ....

http://en.wiktionary.org/wiki/isosceles_triangle

i fail to understand the logic of these old guys .... is there a specific property of isosceles traingle, which is not applied to equilateral triangle..... i mean even 300 years ago, these guys were very intelligent and if they have defined is this way there has to be a logic ... right ?
Director
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Re: geometery confusion [#permalink]  30 Jul 2008, 21:48
AGREE .... All I can say is that ...this is GMAT ... so lets say that OG is GOD and whatwever OG says is true.

"the Official Guide defines an isosceles triangle as one with 'at least two equal sides', so equilateral triangles are officially isosceles on the GMAT"
Re: geometery confusion   [#permalink] 30 Jul 2008, 21:48
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# If two angles of a triangle are equal, is the triangle

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