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

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Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink] New post 16 Jun 2011, 15:24
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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

Solve!
[Reveal] Spoiler: OA

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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 16 Jun 2011, 15:37
I think the answer is A as (1) is enough. A square is a also a quadrilateral and has equal sides. Hence (2) is not enough. I am astounded by OA.
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 16 Jun 2011, 19:00
gijoedude, a square is a rhombus, so 2 is sufficient as well.
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 16 Jun 2011, 19:27
a considering a kite,the diagonals will be perpendicular but not bisecting. Hence sufficient.

b a square is also a rhombus.

D it is.
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 17 Jun 2011, 06:42
Got it. Thanks all!
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 17 Jun 2011, 18:45
1. Sufficient

diagnols are perpendicular bisectors. can only happen in a square or rhombus. Square is a kind of rhombus.

2. Sufficient

As we know its a square or rhombus. Square is a kind of rhombus.

Answer is D.
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Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink] New post 29 Jan 2013, 07:59
gijoedude wrote:
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD



A rhombus is a quadrilateral with all its sides equal to each other.

1.
Imagine that the point where the bisectors meet is called X.
Then, BX = DX and AX = CX.

Using the Pythagorean Theorem you could imagine getting the hypotenuse of sides BX and CX.
Since AX = CX, then the hypotenuse of BX and AX is also as long as the previous.
As you could imagine, all the hypotenuse formed are equal, thus forming equal 4 sides. Hence, a rhombus.

SUFFICIENT.

2.

All sides are equal.

SUFFICIENT.

Answer: D
Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD   [#permalink] 29 Jan 2013, 07:59
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