Question 1021050
Line AB has slope {{{m[AB] = (5-2)/(-1+3) = 3/2}}}
Line CD has slope {{{m[CD] = (1+2)/(5-3) = 3/2}}}
==> Lines AB and CD are parallel.

Line BC has slope {{{m[BC] = (5-1)/(-1-5) = -2/3}}}
Line AD has slope {{{m[AD] = (2+2)/(-3-3) = -2/3}}}
==> Lines BC and AD are parallel.

Last thing is to just show that one of the four angles is a right angle. 
Since the slope of line AB, 3/2, and the slope of line CD, -2/3, have a product of -1, it follows that the angle at vertex C is a right angle, and the proof is complete.