You can put this solution on YOUR website!
Let s be the short side of your "rectangle." And let l be the long side. Let d be your diagonal.
Given the pythagorean theorem, your diagonal will be
if your rectangle is indeed a square.
Use s^2 + l^2 = d^2 to find l^2.
then s^2 +l^2 = 2s^2 and thus l^2 = s^2, hence l=s.
Since your long side and short side are actually the same length, then the rectangle is also a square.
Does this make sense?
I see your teacher said without side lengths.
A rectangle can be broken into two triangles.
If the two sides are the same, then the two corresponding angles will be the same. Namely, they will both be 45º.
Check the angles formed by the triangle. If one of the angles is 45, then you're set. It would be a square.