If vector AB = vector DC, then ABCD is a parallelogram? Is that right? Maybe it's not collinear

If vector AB = vector DC, then ABCD is a parallelogram? Is that right? Maybe it's not collinear

If vector AB = vector DC, then ABCD is a parallelogram,
It is possible to be collinear, given the premise is the quadrilateral on the right

If the quadrilateral ABCD is a parallelogram, then the vector AB = the vector DC, and vice versa
Senior two mathematics, simple judgment
If the quadrilateral ABCD is a parallelogram, then the vector AB = the vector DC, and vice versa
Is this right or wrong? Please answer

Wrong

In the known parallelogram ABCD, O is the intersection of diagonals. Prove: vector Bo = 1 / 2 (vector Ba + vector BC)

Because ABCD is a parallelogram
So vector Ba + vector BC = vector BD, Bo = 1 / 2bd
So vector Bo = 1 / 2 vector BD
=1 / 2 (vector Ba + vector BC)

Let m be the intersection of diagonal lines of parallelogram ABCD and o be any point in the plane of parallelogram ABCD, then (vector) OA + ob + OC + OD=

M is the intersection of parallelogram ABCD diagonal
Vector OA + vector OC
=2 vector OM
Vector ob + vector OD
=2 vector OM
(vector) OA + ob + OC + od = 4 vector OM
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As shown in the rectangular ABCD, the diagonal lines AC and BD intersect at point O, and m and N are the midpoint of OA and ob respectively

The condition you give is not enough to prove BM = CN, because if you want to prove that they are equal, a huge shape must be a regular quadrilateral. The condition you give can't prove that it is a regular quadrilateral!