Question

The proof that HG ≅ EG is shown. Given: G is the midpoint of KF KH ∥ EF Prove: HG ≅ EG 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

Answer 1

The answer is ASA

Explanation:

Edge 2022

Answer 2

In the proof we see that ∠EGF is congruent to ∠HGK because they are vertical angles.  We also see that KG is congruent to FG because G is the midpoint.  Additionally we have that ∠F is congruent to ∠K because they are alternate interior angles.  We have two angles and the side between them, or ASA.