Hello, I am stuck on a problem that at the conceptual level makes perfect sense. Here's the problem:

Use vectors to show that the diagonals of a parallelogram have the same length if and only if the parallelogram is a rectangle. (Hint: letaandbbe vectors along two sides of the parallelogram. Express vectors running along the diagonals in terms ofaandb.)

I have attached a picture. I can let:

d1=a+b

d2 = b-aI know that I am trying to prove that:

$\displaystyle \|d1\| = \|d2\|$

When $\displaystyle \cos\theta = 0 $ for the angle betweenaandb.

Most of my work so far essentially amounts to me plugging in for the Angle Between Two Vectors formula and coming out withadotted withb= 0. This occurs if either is the0vector or if they are perpendicular. However, this doesn't help me with the length ofd1andd2. I am not sure how I can relate the two together. Thanks for any assistance.