VTMO 2016 — Grade 7 — final Question 6

$AB \lt AC$. $E$ lies beyond $B$ on ray $AB$ with $BE = AC$; $F$ beyond $C$ on ray $AC$ with $CF = AB$. $M$ is midpoint $BC , N = AM \cap EF , D = NC \cap EM$. Prove $MA = MN$ and $AN = DF$.