SOLUTION: in a quadrilateral ABCD , angle B = 90°. If {{{AD^2=AB^2+BC^2+CD^2}}}, then prove that angle ACD = 90°

 
We know that ABC is a right triangle because angle B = 90°
So we can use the Pythagorean theorem on that right triangle:



We are given that 



Not that the terms I've colored red are the same in both
equations so we can substitute  for the two red
terms in the second equation,

 

Now we use the converse of the Pythagorean theorem which
states that the Pythagorean theorem holds ONLY for right 
triangles, thus triangle ACD is a right triangle and angle
ACD is a right angle or 90° 

Edwin