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?