A triangle, $ABC$, has point, $M_1$, $M_2$, $M_3$, where $M_1$ is the mid point of Line $AB$, $M_2$ is the mid point of Line $BC$, and $M_3$ is the mid point of Line $AC$.
A smaller triangle, $M_1M_2M_3$, was formed with vertices $M_1$, $M_2$, and $M_3$.
How do I prove that for all different triangle, it will always get $AB=2M_2M_3$, $BC = 2M_1M_3$, $AC = 2M_1M_2$?
Assuming you're allowed to use the parallel postulate:
Try to prove that the segment $M_2M_3$ is parallel to $AC$. Then do the same for the other two inner segments. Then you can prove that all FOUR of the smaller triangles are similar to the large one, and you're on your way.
BTW: I've given a hint here because you selected the self-learning tag, and I figured you'd rather have a nudge in the right direction rather than a complete answer, but correct me if I'm wrong.