Answer
The diagonals are perpendicular.
Work Step by Step
The diagonals can be represented as: $(a+b)$ and $(a-b)$.
$(a+b) \cdot (a-b)= (a \cdot a)- (b \cdot b)$
$(a \cdot a)- (b \cdot b)=|a|^2-|b|^2$
A vector dotted with itself is its length squared, and as we know that the side lengths are equal to each other, so $|a|^2-|b|^2=0$
As the dot product of diagonals is $0$, the diagonals are perpendicular.
