ABCD is a parallelogram with AB parallel to DC. Let AB = a and AD = b.(a) Express AC and BD

ABCD is a parallelogram with AB parallel to DC. Let AB = a and AD = b.
(a) Express AC and BD in terms of a and b.
(b) Simplify (a + b)(b - a).
(c) Hence show that if ABCD is a rhombus then its diagonals are perpendicular.