Because PE//AB PF//AC, angle BAD= angle EPD, angle CAD= angle FPD,

Because AD is the bisector of angle BAC, angle BAD= angle CAD and angle EPD= angle FPD.

Because DG is perpendicular to EP DH and FP, angle DGP= angle DHP.

According to the triangle congruence theorem, PD is the same side and the two angles are equal, so the triangle DGP and the triangle DHP are congruent, so GD=HD, and the distance from D to PE is equal to the distance from D to DF.