Math Paper 32 CIE A level

I just came here to ask, is a square a rhombus? Or are they "mutually exclusive" shapes? Because I proved ABCD, that is already KNOWN as a parallelogram, is a rhombus by proving that AC is perpendicular to BD. This is a valid method, right? Since the only two shapes that have their diagonals perpendicular are rhombuses and kites, right? And since ABCD is a parallelogram, then ABCD MUST be a rhombus, right?

People have been telling me that a square is not a rhombus and it's driving me crazy.. Even if it IS a square, all the question asks is to prove that ABCD is a rhombus, so even if ABCD IS a square, a square is a rhombus, right?

I'm going bonkers, I apologise..

Yep. And I can remember 2.5 and 0.644 as well... Only thing being that I wrote 0.65 (I hate significant figures )

Any shape with four sides is a parallelogram which includes square.

AC can not be perpendicular to BD. Though I didn't do it, rhombus actually has no 90 degree angles so we have to use dot product to show that the two direction vectors aren't equal to 0. I just proved the lengths are equal which should give one mark and finding OD would be another 1 or 2 marks.

AC and BD are the diagonals of the quadrilateral; proving that the diagonals in the parallelogram (you know what I'm talking about, right?) are equal makes it a rhombus, no?

EDIT: The diagonals I'm talking about don't mean the sides of the quadrilateral, but the two lines in the quadrilateral you can make through two opposite points in that quadrilateral..

Yea I get what you mean. But the diagonals can also prove it to be a square. What we need to do is to distinguish from a square.

what about statistics 72 (CIE) ? do you know any forum or page where I could find/discuss the answers?

I felt it was a bit harder, hoping for a mid 50 treshold. Do you guys remember you answers?