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## Homework Statement

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

## Homework Equations

**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?

Thanks