Question

what is the missing reason in the proof?

statement	reason
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:

We have two pairs of angles ($\angle EGF\cong\angle HGK$, $\angle F\cong\angle K$) and a pair of included - sides ($FG\cong KG$) that are congruent. The Side - Angle - Side (SAS) congruence postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, for $\triangle FEG$ and $\triangle KHG$, we have the side - angle - side combination of congruent parts.

Answer:

A. SAS