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# This might be a repetition. Is quadrilateral ABCD a rhombus?

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This might be a repetition. Is quadrilateral ABCD a rhombus? [#permalink]  14 Oct 2009, 21:09
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This might be a repetition.

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

(2) AB = BC = CD = AD
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Re: rhombus? [#permalink]  14 Oct 2009, 21:15
IMO E.

State 1) It can be a Square.
State 2) It can be a Square again.

Together the statements are not sufficient to answer if this is a rhombus or a square.
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Re: rhombus? [#permalink]  14 Oct 2009, 21:24
By definition, square is a special case of rhombus. So all squares can be called rhombi too
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Re: rhombus? [#permalink]  14 Oct 2009, 21:29
So you mean that the answer is C?
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Re: rhombus? [#permalink]  14 Oct 2009, 21:33
I am just throwing pointers, we need to discuss. I do not know what is the ans
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Re: rhombus? [#permalink]  14 Oct 2009, 21:36
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Re: rhombus? [#permalink]  14 Oct 2009, 21:40

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

(2) AB = BC = CD = AD --> rhombus

Or am I missing something, seems pretty obvious...
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Re: rhombus? [#permalink]  14 Oct 2009, 21:45

Well:
(1) True for square or for rhombus but every square is a rhombus, so sufficient
(2) Again true for square or for rhombus but every square is a rhombus, so sufficient

D
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Re: rhombus? [#permalink]  25 Oct 2009, 07:00
about the 2nd option. can't it be a parellogram too?
and a pllgram is not necessarily a rhombus.

so the answer shud be A.
(or am i missing the obvious here??)
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Re: rhombus? [#permalink]  25 Oct 2009, 10:15
any rhombus has the following two properties:
Opposite angles of a rhombus have equal measure.
The two diagonals of a rhombus are perpendicular.

so any square is a rhombus hence D.
Re: rhombus?   [#permalink] 25 Oct 2009, 10:15
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# This might be a repetition. Is quadrilateral ABCD a rhombus?

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