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

xa + yb : xc + yd = b : d

If (7a + 8b)(7c - 8d) = (7a - 8b)(7c + 8d);

prove that a : b = c : d.

If (a + b + c + d)(a - b - c - d) = (a + b - c - d)(a - b + c - d);

prove that : a : b = c : d.