Any rhombus has its diagonals meet at 90 degree angles. The proof for this is a bit lengthy, so I'll let you handle it. The basic idea is to draw in the diagonals, which forms smaller triangles. Proving those triangles to be congruent leads to supplementary congruent angles, which in turn leads to the 90 degree angles needed.
A square is a special type of rhombus where all four angles are the same (each 90 degrees). Put another way, a square is both a rectangle and a rhombus at the same time.
Some rectangles are not squares, so the non-square rectangles will have the diagonals not be perpendicular.
