Question

It is given that the diagonals AC and BD of the quadrilateral ABCD bisect each other at O, i.e the diagonals intersect at O, and O is the midpoint of both AC and BD. Let OA = a and OB = b. Express OC, OD, AB and DC in terms of a and b. Deduce that the quadrilateral ABCD is a parallelogram

Answer 1

AB = OA - OB = b -a
DC = OC - OD = -a - (-b) = b - a
==> AB = DC, thus sides are parallel (1)
BC = -a - b
AD = -b - a = -a - b
==> BC = AD, thus sides are parrallel (2)
by (1) and (2) ABCD is a parallelagram.
This is what I get but think i'm not confident it is right