1. The problem statement, all variables and given/known data Let A, B, C be the vertices of a triangle in the plane and let a, b, c be respectively, the midpoints of the opposite sides. Show that Aa+ Bb+ Cc = 0 (all of them have vector signs on the left). 2. Relevant equations definition of plane 3. The attempt at a solution Drew the picture which would look like a triangle within a triangle. The form Aa... looks most like the component equation but I don't understand how a, b, c equates to x, y, z.