Proof question in geometry

Question

In the figure, segment CF is the angle bisector of angle ACE and angle AFE, prove that segment CF bisects segment AC.

PLEASE help!

Unfortunately,

I can not input the picture, there is no feature for that.

Answer 1

Try this

What you have, I think, is a quadrilateral ACEF with CF bisecting the angle at C and the angle at F.

That makes triangle ACF congruent to triangle ECF by ASA

Then AC=EC and AF=EF because they are corresponding parts of congruent triangles.

That makes CF the perpendicular bisector of AE because points C and F are both equidistant from the endpoints of AE.