The question is a follows.
Midpoints of the sides of a quadrilateral are the vertices of a paralleogram. Determine under what conditions this parallelogram will be (1) a rectangle, (2) a rhombus, (3) a square.
I tried this for my hw question but I am not sure if it was right. For (1), I think the two diagonals have to be perpendicular to each other, for (2), I wrote that the quadrilateral has to be rectangle. And for (3) I wrote that the quadrilateral has to be both (1) and (2). Can someone explain if this argument is right?? And if possible, can anyone give simple proof for this?