Proving four points give a parallelogram (is two vectors being parallel enough?) Let's say that I am given four points and I want to prove they form a parallelogram. What I usually see in books is that they calculate $\vec{AB}$ and show that it is equal to $\vec{DC}$, but they also show that $\vec{BC}$ is equal to $\vec{AD}$.
However, if we can prove that $\vec{AB} = \vec{DC}$, isn't it enough to prove that we have a parallelogram? What would be a counter example?
Thanks.

In general, we have $\vec{AB}+\vec{BC}=\vec{AC}=\vec{AD}+\vec{DC}$, so when $\vec{AB}=\vec{DC}$, we automatically also have $\vec{BC}=\vec{AD}$.
