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. ?

Explanation:

Step1: Recall triangle congruence criteria

We have two angles and the included side.

Step2: Check the given information

We have \(\angle EGF\cong\angle HGK\), \(\angle F\cong\angle K\), and \(FG\cong KG\). This satisfies the ASA (Angle - Side - Angle) congruence criterion.

Answer:

ASA (Angle - Side - Angle)