Answer:
Definitely we can't prove that triangle DFG is congruent to MNP. The reason is because the angles that are congruent don't match the corresponding vertex, that is, the corresponding vertices of these triangles are as follows:
D is corresponding to M
F is corresponding to N
G is corresponding to P
But the angle we know in the first triangle lies on vertex D while on the second triangle the angle lies on vertex P but it should lies on vertex M, so we'd prove they are congruent by Side-Angle-Side Postulate (SAS).
