pl solve ths.. exam next week

[gmat20092009]

Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD


OA is given D.....My ans is C

My question is like rhombus,kite also has perpendicular bisectors.
A kite is not a rhombus cos kites sides are not all equal like rhombus.

This is a manhattan test question

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The first is true coxz the diagonals are perpendicular bisectors


the second seems true as all sides are equal (though at first instinct ul feel it duc b a square also, but square is a special kind of rhombus)

Thats the only feasible explanation accordin to me....

hope im rite!