Use Vectors To Show Three Vertices Belong to a Right Triangle The Full Question

Theorems Used
This is what I call theorem 1:

My Work
This problem has two major steps as far as I can see. First, I must show that these are points of a triangle(not specifically a right triangle). Second, I will use theorem $1$ to show that there exists a $90$ degree angle between two of my vectors, which means my triangle is right angle triangle. 
Where I Am Having Difficulty
The second step is fine for me, but I'm having trouble finding necessary and/or sufficient conditions to show that these are the vertices of any triangle. I'm wondering if anyone knows some vector rule or theorem that I can use to show that these are the vertices of a triangle. Thanks.

Any three points not contained in a single line form a triangle. If points were contained in the same line, then their difference vectors would all be parallel.
