We have to prove that triangles EFI and HFG are congruent.
We are given that:
- IE and GH are parallel
- EF and HF are congruent sides.
Then:
1) Statement: IE || GH
Reason: given
2) Statement: EF ≅ HF
Reason: given
3) Statement: Reason: vertical angles
4) Statement: GF ≅ IF
Reason: F is the midpoint of segment GI
5) Statement: ∆EFI ≅ ∆HFG
Reason: SAS postulate