proofing

A (0,0)

B (b,c)

C (b+ sqrt(bsq + csq), c)

D (sqrt(bsq + csq), 0)

First......let's consider the slope of AC, one of the diagonals....we have

 ([b + √b^2 + c^2] - 0 ) / {c - 0)  =   ([b + √b^2 + c^2] / c  

Next, let's consider the slope of the other diagonal, BD.....we have

[ 0 - c ] / (  ([b + √b^2 + c^2 ] - b ) =  -c / ([b + √b^2 + c^2]

And since the slopes are negative reciprocals, the diagonals are perpendicular to each other