1. ## Vector addition triangle medians

"In a triangle, let u, v, and w be the vectors from each vertex to the midpoint of the opposite side. Use vector methods to show that u + v + w = 0."

I found an answer to the problem here, but I am still confused. Could someone explain the logic in a little more detail?

2. Suppose that $\vec{a},~\vec{b},~\&~\vec{c}$ are the sides of the triangle.
Then in some order we would have $\vec{u} =\vec{a}+0.5 \vec{b},~\vec{v} =\vec{b}+0.5 \vec{c},~\&~\vec{w} =\vec{c}+0.5 \vec{a}$.

Notice that $\vec{a}+ \vec{b}+ \vec{c}=0$.

3. Forgive me, I may have forgotten (or never learned) the rule that is be critical to this problem. Is it a generally understood fact that the vector sum of the sides of a triangle is 0 (i.e. this is not something that I would have to prove in my answer)?

4. Disregard my last post. I get it. Thank you very much!