Why is this statement NOT always true?:

Question

The longer diagonal of the rhombus is perpendicular to two sides of the rhombus.

Answer 1

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.