A hard question about the basic proportionality theorem

[raw nest]

ABCD is a trapeze such that the 2 lines (AD) and (BC) intersect with each other in point E. M is a point that belongs to the segment [DC] and N is another point that belongs to the half-line [DC) such that:
DN>DC and CN=DM and the two lines (AM) and (BM) intersect with each other in point F.
SHOW THAT THE TWO LINES (EF) AND (AB) ARE PARALLEL LINES

[safe knoll]

I can solve this without intercept theorem

I am using ∆ as a symbol for denoting angles

[raw nest]

@safe knoll wdym?

[safe knoll]

Wait where did the solution go

Ughhh

Gotta write it all over

[raw nest]

@garvitaneja so?