I'd say it's never true.
The diagonals of a rhombus are perpendicular bisectors of each other. So, unless the shorter diagonal is parallel to a side, the longer cannot be perpendicular. Since the diagonals are transversals between parallel sides, they cannot pe parallel to them.
Why is this statement NOT always true?:
The longer diagonal of the rhombus is perpendicular to two sides of the rhombus.
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