Statement → Reasons
1. DF = EG → Given (because this is a given information in the proof).
4. DE + EF = EF + EG → Substitution Property of Equality
Statement 4 uses substitution property of equality that is based on Statement 1, 2, and 3. Since Statement 2 said DF = DE + EF then, we can substitute the DF in Statement 1 with DE + EF.
Similarly, Statement 3 says EG = EF + FG, then we can replace EG in Statement 1 with EF + FG.
Thus, making the statement 4 DE + EF = EF + FG.
5. DE = FG → Segment Congruence Postulate
Since Statement 4 has a common segment that is EF and both sides are equal, that just shows that what is being added to EF which are DE and FG are also equal too.
