Show Triangle Midpoints Sum to Zero

[IL0VEMATH]

Let A', B', C' be the midpoints of the sides BC, CA, AB of the triangle ABC. Show that \overline{AA'}+\overline{BB'}+\overline{CC'}=\overline{0}

 

[Lord Crc]

Have you tried writing out the formula for the midpoints in terms of the vertices A,B,C and inserting this into the equation?