Giả sử 
`(a + b)/(b + c) = (c + d)/(d + a)`
`=> 1 + a/c = 1 + c/a`
`=> a^2 = c^2`
`=>` \(\left[ \begin{array}{l}a = c\\a = -c\end{array} \right.\) 
Mặt khác:
`(a + b)/(c + d) = (b + c)/(a + d)`
`=> (a + b)/(c + d) + 1 = (b + c)/(a + d) + 1`
`=> (a + b + c + d)/(c + d) = (a + b + c + d)/(a + d)`
`=> a + b + c + d = 0`