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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]

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16 Oct 2006, 11:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Triangle ABC has three angles, x, y and z.

Is ABC isosceles?

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

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16 Oct 2006, 11:58
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

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Director
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16 Oct 2006, 11:58
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

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Senior Manager
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16 Oct 2006, 11:59
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.

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Manager
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16 Oct 2006, 12:09
Why can it not be equilateral and therefore C?

If y=z, we do not know x?

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16 Oct 2006, 12:18
Every equilateral triangle is an isoceles triangle..

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Director
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16 Oct 2006, 12:18
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.

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Manager
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16 Oct 2006, 12:19
The learning never ends...thanks.

But every equilateral is still isosceles, right or wrong?

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16 Oct 2006, 12:29
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

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Manager
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16 Oct 2006, 21:46
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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16 Oct 2006, 21:46
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# Triangle ABC has three angles, x, y and z. Is ABC isosceles?

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