The missing reasons that complete the proof are: 4. reflexive property of congruence. 5. SAS congruence theorem.
What is the SAS Congruence Theorem?
The SAS Congruence Theorem asserts that when the two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of a second triangle, then it can be proven or stated that both triangles in question must be congruent to each other.
In this case, based on what has been established already and the information given, we will have that:
side FI ≅ side FI based on the reflexive property of congruence.
ΔFGI ≅ ΔFHI based on SAS theorem.