use the following properties of quaderilaterals to determine the following riddle.

i have 2 sets of parallel sides. My diagonals are angle bisectors. My diagonals are perpendicular. Two of my angles are 60 degrees. who am I?

ok, well i have narowed it down to two shapes, a rhombus, and a parallelogram, now i have to deside which one works. hmmmmm.....

well i know that a rhombus has the diagonals are angle bisectors,and my angles are perpendicular, but that is now information.

so what should i use to fugure the rest of it out?