Problem: In ΔABC, D is on segment BC, E is on AC and F is the intersection of segments EB and AD. Assume further that AC ≅ BC and EC ≅ DC. Prove ΔAFE ≅ ΔBFD.
The picture is given as an attachment.
* 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 segment BC, E is on AC
F is the intersection of segments EB and AD
2. AFB ≅DFB 2. Vertical angles
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.
6.AB≅AB 6. Reflexive property
7. △ADB≅ △AEB. 7. SAS postulate
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.