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# Triangle ABC has three angles, x, y and z. Is ABC isosceles?

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Manager
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Triangle ABC has three angles, x, y and z. Is ABC isosceles? [#permalink]  16 Oct 2006, 10:54
Triangle ABC has three angles, x, y and z.

Is ABC isosceles?

1) (x+y) - (x+z) = 0
2) (y+z) - (y+x) = 0
SVP
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Triangle ABC has three angles, x, y and z.

Is ABC isosceles?

1) (x+y) - (x+z) = 0
2) (y+z) - (y+x) = 0

FORM ONE

Y-Z = O IE Y=Z ANGLES CAN NEVER BE ZERO ....SUFF

FROM TWO

Z =X ......SUFF

Director
Joined: 23 Jun 2005
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D

Statement 1:
x(y-z) = 0
x cannot be 0. So, y=z. SUFF

Statement 2:
y(z-x) = 0

y cannot be 0. So, z=x. SUFF
Senior Manager
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Re: Is it Isosceles? [#permalink]  16 Oct 2006, 10:59
Rayn wrote:
Triangle ABC has three angles, x, y and z.

Is ABC isosceles?

isosceles = two angles or two sides are equal.

1) (x+y) - (x+z) = 0
2) (y+z) - (y+x) = 0

1) x+y-x-z=0 , y = z , so angles y and z are equal. yes.
2) y+z-y-x=0, z=x, so angles z and x are euqal. yes.

D, EACH is SUFF.
Manager
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Why can it not be equilateral and therefore C?

If y=z, we do not know x?
Director
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Every equilateral triangle is an isoceles triangle..
Director
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Rayn wrote:
Why can it not be equilateral and therefore C?

If y=z, we do not know x?

Since the question is "Is ABC isosceles?", we do not need to worry whether it is equilateral or not.
Manager
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The learning never ends...thanks.

But every equilateral is still isosceles, right or wrong?
Senior Manager
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Agree D, yep all equi's count as iso's:

http://en.wikipedia.org/wiki/Triangle

Quote:
In an isosceles triangle at least two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side). An equilateral triangle is actually also an isosceles triangle, but not all isosceles triangles are equilateral triangles
Manager
Status: Post MBA, working in the area of Development Finance
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londonluddite wrote:
Agree D, yep all equi's count as iso's:

http://en.wikipedia.org/wiki/Triangle

Quote:
In an isosceles triangle at least two sides are of equal length. An isosceles triangle also has two equal internal angles (namely, the angles where each of the equal sides meets the third side). An equilateral triangle is actually also an isosceles triangle, but not all isosceles triangles are equilateral triangles

I think the quote clarifies the doubt ( I myself seemed to have forgotten my geometry!)
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