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# Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD

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Director
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Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink]  16 Apr 2006, 13:01
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Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD

Hopefully this can lead to discussions on more details on Parallelograms, and what properties are enough to know the diagrams?
Manager
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[#permalink]  16 Apr 2006, 13:21
Hmmn, I'm shooting for E. I think the statements could fit a square or a rhombus.
Senior Manager
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[#permalink]  16 Apr 2006, 14:01
Based on given property it could be square or rhombus.

E
Manager
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[#permalink]  17 Apr 2006, 12:49
gmat_crack wrote:
Based on given property it could be square or rhombus.
E

That's true, but since a square is only a special case of a rhombus,
it is C.
Director
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[#permalink]  17 Apr 2006, 20:23
Well the official answer is D...

it could be either.. its from manhattan..

if the diagonals are perpendicular bisectors, then it is a square or rhombus.. and if all the sides are equal too, it is square and rhombus..

a tough one.. i did E orignally..

but then when i looked at it.. it makes sense rthe question already gives us the information that its a quadrilateral.. so its a 4 sided figure...
VP
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[#permalink]  18 Apr 2006, 22:44
Nice question. D is obvious after the explaination
VP
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[#permalink]  19 Apr 2006, 03:46
willget800 wrote:
Well the official answer is D...

it could be either.. its from manhattan..

if the diagonals are perpendicular bisectors, then it is a square or rhombus.. and if all the sides are equal too, it is square and rhombus..

a tough one.. i did E orignally..

but then when i looked at it.. it makes sense rthe question already gives us the information that its a quadrilateral.. so its a 4 sided figure...

So if it is either of them how could it be Rhombus? Shouldnt the answer be E?
Senior Manager
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[#permalink]  19 Apr 2006, 05:18
E from the given data, figure can be rectangle/rhombus
Senior Manager
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[#permalink]  19 Apr 2006, 05:22
Square has all internal angles 90 right?

Square is a rhombus with all angles 90. right?

So, from the given data figure can be rhombus or sqare? and logically they are different figures. I have come across lots of rectangle and sqare problems causing same type of confusion but in those questions we look for exact specs.
Director
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[#permalink]  19 Apr 2006, 17:19
square is a type of rhombus..

i was suprised manhattan put this question on a 500 to 600 bucket.. surely it is not!!!!!!!!!!!!!!!!!!
Intern
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[#permalink]  19 Apr 2006, 18:12
willget800 wrote:
square is a type of rhombus..

i was suprised manhattan put this question on a 500 to 600 bucket.. surely it is not!!!!!!!!!!!!!!!!!!

I still did not understand, how it is D.

Quadrilateral means a four sided figure. It can be a square too. Square is a type of quadrilateral. How do you say "D" is correct?
Senior Manager
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[#permalink]  19 Apr 2006, 18:48
[quote="willget800"]Well the official answer is D...

it could be either.. its from manhattan..

if the diagonals are perpendicular bisectors, then it is a square or rhombus.. and if all the sides are equal too, it is square and rhombus..

a tough one.. i did E orignally..

but then when i looked at it.. it makes sense rthe question already gives us the information that its a quadrilateral.. so its a 4 sided figure...[/quote]

Answer could be A
SVP
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[#permalink]  19 Apr 2006, 20:34
Square is a very special quadrilateral. It can be seen as a special type of parallelogram, a special rectangle, and a special rhombus.

As for crossed quadrilaterals, I do not believe that it is possible that all of its sides are equal. Let's use the shape in the link you provided, ADBC. If AC=AD then angle ACD=angle ADC. If BC=BD, then angle BCD=angle BDC. However we also know that angle ACD < angle BCD and angle ADC > angle BDC. You can see that if the two angles in the right hand side are equal, then the angles in the left hand side can NOT be equal.
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Senior Manager
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[#permalink]  23 Apr 2006, 10:02
true.

Cross quadrilaterals with all equal sides is impossible to draw in one plane.

Thanks Hong Hu for making me thing some more
[#permalink] 23 Apr 2006, 10:02
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# Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD

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