Because EF is the middle vertical line of AD.

So: the triangle EAD is an isosceles triangle, and the angle EAD = the angle ADE.

Because: AD is the bisector of triangle ABC

So: angle DAB= = angle DAC

To sum up: angle EAC= = angle EAD- angle DAC= = angle ADE-angle DAB= = angle B.

(2)

Because EF is the middle vertical line of AD.

So: the triangle FAD is an isosceles triangle, and the angle FAD = the angle FDA.

Because: AD is the bisector of triangle ABC

So: angle FAD= = angle DAC

So: angle FDA= = angle DAC

So: FD is parallel to AC.