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

(2) AB = BC = CD = AD

1) is necessary and sufficient condition for rhombus 2) is also same.

guess D

its not necessary that a figure with diagonals bisecting each other at rt angles is rhombus,may be its sides are unequal.we can try this drawing on a paper. hence (2) is important
_________________

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

(2) AB = BC = CD = AD

1) is necessary and sufficient condition for rhombus 2) is also same.

guess D

its not necessary that a figure with diagonals bisecting each other at rt angles is rhombus,may be its sides are unequal.we can try this drawing on a paper. hence (2) is important

No.. if the diagonals are perp and bisect each other, then it has to be a rhombus. Distance from any vertex to the adjoining vertex will beI same. Can be proved using the congruence of the 4 triangles using SAS (side angle side) approach.