(1) The sides of Q have the same length.
insuff: could be a rhombus or a square
(2) The diagonals of Q have the same length.
insufficient: could be a rectangle or square
combine: sufficient, both are only possible in case of square
I always thought diagonals of a rhombus are also equal in length! Or am I wrong?
Yup, I had a big misconception...Diagonals of a rhombus are not necessarily equal in length, they have only two properties:
1) They bisect each other.
2) They are perpendicular to each other.