(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the diagonals of a paraelogram are perpendicular iff the parallelogram is a rhombus.

2. Relevant equations

a(dot)b= 0

3. 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,aandbthat form the corner of a rhombus, then that means that the magintude ofaandbare equal. By inspection of a diagram of this vector problem, I found that (a+b) (dot) (a-b) = 0 iff the magintude ofaandbare 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?

Thanks

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# Homework Help: Vector Rhombus Proof

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