Answer
If the diagonals of a given rectangle are perpendicular, the shape is a square.
Work Step by Step
We name the vertices:
$A:(0,0) \\ B: (0,b) \\ C: (a,b) \\ D: (a,0)$
We see if a is equal to b. Since the lines are perpendicular, it follows that the product of their slopes is $-1$:
$ m_1= \frac{b-0}{a-0} = \frac{b}{a}$
$ m_2= \frac{b-0}{0-a} = \frac{b}{-a}$
Thus:
$\frac{b}{-a} \times \frac{b}{a} = -1$
This is only true when a and b are equal, so we see that the shape is a square.
