If a : b = c : d, prove that :

(i) 5a + 7b : 5a - 7b = 5c + 7d : 5c - 7d

(ii) (9a + 13b)(9c - 13d) = (9c + 13d)(9a - 13b)

(iii) xa + yb : xc + yd = b : d