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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]

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16 Apr 2006, 14:01
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

(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?

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Manager
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16 Apr 2006, 14:21
Hmmn, I'm shooting for E. I think the statements could fit a square or a rhombus.

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Senior Manager
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16 Apr 2006, 15:01
Based on given property it could be square or rhombus.

E

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Manager
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17 Apr 2006, 13:49
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.

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Director
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17 Apr 2006, 21:23
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...

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VP
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18 Apr 2006, 23:44
Nice question. D is obvious after the explaination

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VP
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19 Apr 2006, 04:46
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?

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Senior Manager
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19 Apr 2006, 06:18
E from the given data, figure can be rectangle/rhombus

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Senior Manager
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19 Apr 2006, 06:22
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.

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Director
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19 Apr 2006, 18:19
square is a type of rhombus..

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

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Intern
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19 Apr 2006, 19:12
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?

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Senior Manager
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19 Apr 2006, 19:48
[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]

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SVP
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19 Apr 2006, 21:34
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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23 Apr 2006, 11:02
true.

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

Thanks Hong Hu for making me thing some more

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23 Apr 2006, 11:02
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