Question

gj ≅ hi and hi || gj. complete the proof that △gjk ≅ △ihk.
1 gj ≅ hi given
2 hi || gj given
3 ∠gkj ≅ ∠hki vertical angle theorem
4 ∠j ≅ ∠h alternate interior angles theorem
5 △gjk≅△ihk

Explanation:

Step1: Identify known congruences/angles

We have $\overline{GJ} \cong \overline{HI}$ (given), $\angle J \cong \angle H$ (alternate interior angles), and $\angle GKJ \cong \angle HKI$ (vertical angles).

Step2: Apply AAS congruence

Two angles and a non-included side of $\triangle GJK$ are congruent to the corresponding two angles and non-included side of $\triangle IHK$.

Answer:

AAS Congruence Theorem