Question

What is the missing step for Given: △AFC≅△EFC, BC ≅ DC and ∠GHF≅∠GIF. Prove: △AHB≅△EID. 1
triangle, A, F, C, \cong, triangle, E, F, C△AFC≅△EFC
start overline, B, C, end overline, \cong, start overline, D, C, end overline
BC
≅
DC

angle, G, H, F, \cong, angle, G, I, F∠GHF≅∠GIF
Given
2
start overline, A, C, end overline, \cong, start overline, E, C, end overline
AC
≅
EC

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
3
start overline, A, B, end overline, \cong, start overline, E, D, end overline
AB
≅
ED

Congruent segments subtracted from congruent segments form congruent segments
4
5
angle, A, H, B, \cong, angle, G, H, F∠AHB≅∠GHF
Vertical angles are congruent
6
angle, E, I, D, \cong, angle, G, I, F∠EID≅∠GIF
Vertical angles are congruent
7 _
angle, A, H, B, \cong, angle, E, I, D∠AHB≅∠EID
Transitive Property
8
triangle, A, H, B, \cong, triangle, E, I, D△AHB≅△EID
AAS

Answer 1

Step 4 should be the given angle congruence restated:

4. ∠GHF ≅ ∠GIF — Given

With that, the chain for the transitive step is:
5. ∠AHB ≅ ∠GHF (vertical angles)
4. ∠GHF ≅ ∠GIF (given)
6. ∠GIF ≅ ∠EID (vertical angles)

So by transitivity ∠AHB ≅ ∠EID (step 7), and then AAS gives △AHB ≅ △EID (step 8).