First, generally, "lines" cannot be described as congruent because they have no definite length, so I think you are describing line segments. Line segments are congruent if their lengths are equal.
Second, I think there is information in your picture that is not being conveyed in the text of the question. I suspect that your picture might look something like this
So a two line proof of this using this figure might look something like this
1. AE ≅ BD Given
2. CD ≅ CE Given
3. AE = BD Def. of congruent segments
4. CD = CE Def. of congruent segments.
5. AE = AC + CE Whole is equal to the sum of its parts
6. BD = BC + CD Whole is equal to the sum of its parts
7. AC + CE = BC + CD Substitution lines 3, 5 & 6
8. AC + CD = BC + CD Substitution lines 4 & 7
9. AC = BC Subtracting CD from both sides of line 8 (Equals subtracted by equals are equal).
10. AC ≅ BC Def. of congruent segments.
The key points to take away from such a proof are to (1) understand relationship between congruence and equality of measure and (2) unpack information from definitions and postulates. Stay warm, and I hope this was helpful. John