Vectors (prove a quadrilateral is a parallelogram)

[crayzwalz]

Homework Statement

The diagonals of quadrilateral ABCD bisect each other. Use vectors to prove that ABCD is a parallelogram.

The Attempt at a Solution

let O = point of intersection

AO = AD + DO
DO = 1/2DB
AO = AD + 1/2 DB

AO = AB + BO
BO = -1/2DB
AO = AB - 1/2DB

2AO = AD + 1/2DB - 1/2DB + AB
AC = 2AO
AC = AD + AB (this is true for parallelograms)

is this solution correct?

 

[crayzwalz]

can anyone verify if this is correct or not pls

 

[Quinzio]

Yes it's correct, but maybe not so "sharp".

I'd have done:
OA = -OC
OB = -OD
AB = OB-OA = OC-OD = CD
AB = CD (opposite sides are parallel, and equal too).