In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?

Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.
A rhombus is a quadrilateral and:
- its opposite angles have equal measure.
- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
- Its diagonals bisect opposite angles.