Problem: In ΔABC, D is on segmentBC, E is onACand F is the intersection of segmentsEBandAD. Assume further thatAC≅BCandEC≅DC. Prove ΔAFE ≅ ΔBFD.

The picture is given as an attachment.

Show △AFE≅△BFD

* Oh anything such as AC≅BC are line segments without the line notation on top of each pair of points. I couldn't figure it out with latex.

Partially completed proof

1. Assume AC≅BC amd EC≅DC. 1. Assumption

D is on segmentBC, E is onAC

F is the intersection of segmentsEBandAD

2. AFB ≅DFB 2. Vertical angles

//EFD ≅AFB

3. AE is congruent to DB 3. derived from step 1

4. CAB≅ CBA 4. Lemma A- In △ABC if AC≅BC then the base angles are congruent

5. △ABC is an isosceles 5. Isosceles triangle theorem- A triangle is isosceles iff the base angles are congruent.

triangle

6.AB≅AB 6. Reflexive property

7. △ADB≅ △AEB. 7. SAS postulate

8.

I almost have everything but I just can't seem to figure these last steps. Somehow I don't know how to show point F where the two line segments EB and AD meet is the midpoint or something.

I got it. I concluded with ASA.