## Elementary Geometry for College Students (7th Edition)

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.