Prove that the diagonals of a paraelogram are perpendicular iff the parallelogram is a rhombus.
a (dot) b = 0
The Attempt at a Solution
This is how I started:
By definition, a rhombus is a quadrilateral with all sides equal in length. So this means that if I have two vectors, a and b that form the corner of a rhombus, then that means that the magintude of a and b are equal. By inspection of a diagram of this vector problem, I found that (a+b) (dot) (a-b) = 0 iff the magintude of a and b are equal.
This is great, however, it will not fly because I cannot just say "by inspection of the diagram" right. How can I put this in words that will make my proof make sense?