Thread: "A parallelogram is a rhombus if and only if its diagonals are at right angles"

I proved that ||a+b|| = ||a-b|| if and only if a.b = 0

However the next part says using this explain why a paralleogram is a rhombus if and only if its diagonals are at right angles..

I can't figure this out?

This is a neat problem.
If are consecutive sides of a parallelogram then are its diagonals.
Now .

So if the parallelogram is a rhombus then .
What does that imply?

What is the converse?

Originally Posted by Plato

This is a neat problem.
If are consecutive sides of a parallelogram then are its diagonals.
Now .

So if the parallelogram is a rhombus then .
What does that imply?

What is the converse?

I understand exactly what you've done so far, but still I don't know what it implies!!!

If the paralleogram is a rhombus then it's diagonals must be at right angles. This means a.b = 0

Now what?!

I frankly do not know what to say to that.
if and only if