Always: that's what makes a rhombus a rhombus.
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Well a rhombus is sometimes and square. but a square is always a rhombus
Always. In fact, one method of proving a quadrilateral a rhombus is by first proving it a parallelogram, and then proving two consecutive sides congruent, diagonals bisecting verticies, etc.
Sometimes. Remember, in order for two polygons to be similar, their angles must be congruent, and their corresponding sides must be proportional. In a rhombus, it is always possible for the angles to differ.
Sometimes
always