Question

what is the missing reason in the proof?
statement reason

1. ∠egf ≅ ∠hgk 1. vert. ∠s are ≅
2. kh || ef 2. given
3. ∠f ≅ ∠k 3. alt. int. ∠s are ≅
4. g is the midpoint of kf 4. given
5. fg ≅ kg 5. def. of midpt.
6. △feg ≅ △khg 6. ?
7. hg ≅ eg 7. cpctc

sas
asa
aas
hl

Explanation:

Step1: Identify matching angles/side

From statements 1,3,5:
$\angle EGF \cong \angle HGK$, $\angle F \cong \angle K$, $FG \cong KG$

Step2: Match to congruence rule

Two pairs of congruent angles and a pair of congruent non-included sides fit AAS.

Answer:

AAS